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Social Institutions: Definition & Examples - Video & Lesson Transcript

Pediatric Palliative Care and Pediatric Medical Ethics: Opportunities and of social institutions, Challenges. The fields of mapp vs ohio significance, pediatric palliative care (PPC) and pediatric medical ethics (PME) overlap substantially, owing to list of social, a variety of historical, cultural, and significance, social factors. This entwined relationship provides opportunities for leveraging the strong communication skills of both sets of of social, providers, as well as the potential for resource sharing and research collaboration. At the same time, the how to become personal and professional relationships between PPC and PME present challenges, including potential conflict with colleagues, perceived or actual bias toward a palliative care perspective in resolving ethical problems, potential delay or underuse of PME services, and a potential undervaluing of the medical expertise required for PPC consultation. We recommend that these challenges be managed by: (1) clearly defining and list of social institutions, communicating clinical roles of PPC and PME staff, (2) developing questions that may prompt PPC and mapp vs ohio, PME teams to request consultation from the institutions other service, (3) developing explicit recusal criteria for PPC providers who also provide PME consultation, (4) ensuring that PPC and PME services remain organizationally distinct, and (5) developing well-defined and broad scopes of practice. Overall, the rich relationship between PPC and significance, PME offers substantial opportunities to list, better serve patients and biography, families facing difficult decisions. pediatrics palliative care medical ethics hospital care Abbreviations: PME — pediatric medical ethics PPC — pediatric palliative care. Prologue A 14-year-old boy, who we will call John, lies in bed. His head and back are propped up by pillows, his breathing appears labored, and his brow glistens with sweat. Next to his bed stands an IV pole with a patient controlled analgesia pump, a long thin clear plastic tube connected to the central venous catheter that protrudes from underneath his shirt.

The room is dark, the shades being drawn and list of social institutions, all but the bathroom lights turned off. Outside, in the hallway, with the door to his room closed, his parents are conversing in an animated manner with the attending physician. They do not want their son to mapp vs ohio significance, be told that the cancer has returned and is now widely spread. At the same time, they recognize how uncomfortable their son is and want all efforts to be made to lessen his pain and ease his breathing. After a fairly lengthy discussion, the parents and the attending physician agree to requesting both a palliative care consultation, to help with pain and of social institutions, symptom management as well as further clarification of goals and limits of care, and an ethics consultation, to shakespeare bio, help think through the pros and cons of telling John the full truth or something less than the full truth. For the of social institutions past several decades, in the realm of pediatric hospital practice, the how to become a contract fields of palliative care and medical ethics have to a large degree overlapped and entwined. Indeed, this special supplement to Pediatrics , 1 of of social institutions, a series of supplements devoted to william shakespeare bio, pediatric ethics, testifies to the particular relevance of pediatric palliative care (PPC) to pediatric medical ethics (PME), and vice versa. In this issue, the reader will find illuminating discussions of the ethical “hot topics” of autonomy, truth telling, futility, the of social role of values in decision-making, the extent of professional duties, and become, the line between the easement of suffering and euthanasia (all fitted out with compelling apt examples from PPC). Even if the of social institutions relationship between PPC and ethics is investment refers, evident, we should not consider the depths of the relationship to be self-evident, nor should we be blase about list institutions, how to best manage aspects of this relationship. Shakespeare Bio? 1 , 2 In this essay, we will explore the reasons for the association (at times verging on an alliance) between PPC and pediatric ethics, consider the advantages and disadvantages of of social, this tight relationship, and offer up some recommendations about web dubois biography, how to manage and make the most of this set of connections (Fig 1). Reasons, opportunities, challenges, and recommendations for of social managing the relationship between pediatric palliative care and pediatric medical ethics.

In writing this essay, one of us is fully aware that he (albeit as a flawed example) personifies this enmeshed relationship, being both a practicing PPC physician as well as a practicing pediatric ethics consultant at significance a large children’s hospital. The reader should also be aware of these facts, as the journey along this dual-path career may have provided not only certain insights but also some personal baggage that may have influenced what we write. The origins and causes of the association between PPC and ethics can be traced to historical and cultural factors, as well as a combination of institutions, self and spencers, social selection. In 1965, the concept of list, using “intermittent positive pressure ventilation” to treat immature infants was born into the world. Investment To? 3 Although physicians had long provided care to list of social institutions, infants who were born well before their due date, the introduction of nora house, intubation and mechanical ventilation led to the creation not only of neonatal intensive care units during the list institutions ensuing decade, but also to a host of pressing ethical dilemmas. Doctors had to decide which premature infants should be treated with this level of high-intensity care. The alternative to intubation, mechanical ventilation, and other invasive neonatal intensive care unit interventions was to biography, provide “comfort care measures,” or what we would today call palliative care.

4. During the 1970s and early 1980s, the list institutions practice of mapp, issuing “do not attempt resuscitation” orders both came into existence and became a focal point for ethical debates about the involvement of parents in the process of making decisions about the medical care that their children receive. Of Social Institutions? 5 Here again, the killer dilemmas about the appropriate ways to care for of social institutions dying children and children who have serious illnesses were the focus of customer, both medical ethicists and of specialists in palliative care. In 1979, the paradigm-altering ethnographic study of the “private worlds of dying children” revealed that children who had advanced cancer often fully understood the grim nature of their prognosis. 6 Even so, the institutions children seldom talked about their thoughts, beliefs, or dreams about dying, death, or an afterlife, maintaining this lonely isolation by a sad dance of “mutual pretense.” Both the children and their parents continued to behave with each other as though everything would be okay to provide support to the person they loved. The ethical concern of truth telling was henceforth apiece with PPC. In 1982, Baby Doe was born with Down syndrome and an esophageal atresia with a tracheal esophageal fistula. After a decision to not operate to correct the atresia was made by economic his parents and physicians, the infant was treated with sedating and pain relieving medications until he died 6 days later. List Of Social? 7 The subsequent outcry and passage of federal regulations underscored again the contentious dilemma of who to treat and how. Web Dubois? More pointedly, the Baby Doe controversy brought to institutions, the fore concerns about biases against disabled individuals, as well as concerns when family interests seem to outweigh the spencers customer service best interests of the child, with both sets of concerns potentially leading to fundamental injustices. 8 , 9.

These examples can be multiplied, illustrating how historically some of the most trenchant issues in pediatric medical ethics have arisen in the context of patients who have grave illness potentially confronting the end of life, with difficult decisions to list, make about how to best care for biography these individuals. The observed historical association of PPC and PME is no coincidence, reflecting instead several aspects of our cultural milieu that make this association likely. List Of Social Institutions? 10 Death is an oddly marginalized topic in American culture, being on the one hand the centerpiece of violent or frightening mainstream entertainment, yet on the other hand being an issue so painful and difficult to contemplate privately or discuss publicly that doing so in a sustained, thoughtful, considered manner is felt by many to be taboo. As a result, even though the investment refers death rate is ultimately 100%, we struggle as a society to institutions, envision the ideal care of dying individuals, to engage each other in significance, formulating plans to assure such care, and to enact these care plans. These struggles are difficult when the patient is a competent adult, and exponentially more difficult when concerning children.

PPC engages in this struggle, patient by patient. Institutions? Such efforts require not only grappling with death, but also with other difficult and a doll's, marginalized issues that are central to PME, such as views regarding the value of life, the list of social institutions degree to which impairments do or do not diminish this value, the spencers service practical and spiritual implications of pediatric suffering, and of social institutions, the pursuit of a path of care that is in the child’s best interest while respecting the child’s emerging capacity to make reasonable decisions that may be contrary to the decisions of the parents. People who engage in PPC and PME also tend to exhibit similar personality characteristics: good collaborative communication skills, a manner of interpersonal interactions perceived by others as especially respectful and kind, an often broadly ecumenical personal world view, and an openness to both joy and sadness. This is not to william bio, say that PPC and PME practitioners have a corner on the market of any of these characteristics, or exhibit all of them to an exemplary degree, but these characteristics do seem to cluster in both of list of social institutions, these sets of practitioners. This clustering may be driven by significance individual self-selection, based on one’s sense of personal interests and list, strengths, or by the encouragement of others. The overlap of PPC and PME, in terms of both core content concerns and personnel with interest and aptitude, presents several advantageous opportunities. Shared Collaborative Communication Skills. A core set of collaborative communication skills enables PPC and PME personnel to have productive and sometimes transformative encounters with patients, parents, and other health professionals. Collaborative communication can help to clarify everyone’s (often differing) sense of the clinical situation, explore and support feelings of mapp vs ohio significance, hope, fear, and frustration, examine the rationale and goals of care, and formulate consensus treatment plans. Such collaborative communication, when empowered by emotional intelligence, can promote a common sense of purpose and respect, and can create shared agendas out of apparent conflict.

Having personnel who are particularly adept at collaborative communication use this skill in both the practice of PPC and PME is a sensible use of of social, a valuable and sometimes limited resource. The fields of PPC and PME can provide cross-fertilization regarding skills and biography, intellectual agendas. The specific collaborative communication challenges confronted by of social institutions practitioners in either PPC clinical consultation or PME ethics consultation can promote the further growth and development of these practice skills in ways that can benefit either realm of practice. Investment? The 2 disciplines also have, as noted, many common areas of interest, presenting opportunities for list institutions scholarly or research collaboration. Some organizations combine palliative care and medical ethics programs, housing them underneath 1 administrative umbrella. Spencers Customer Service? This arrangement, which seems sensible given the overlap of PPC and PME outlined here, permits the colocation of like-minded colleagues and efficient use of of social, support staff and joint program resources. The overlap of house, PPC and PME also presents certain challenges that need to be recognized and of social, managed.

Potential Conflict With Colleagues. PPC sometimes involves conflict among health care colleagues, and nora a doll's, PME consultation sometimes is sought to address and resolve these conflicts. To the list degree that members of the PPC team are also members of the PME consultation service, the handling of the economic case by of social institutions the PME consultation service may appear to be influenced by a conflict of nora, collegial interests. The potential for of social institutions such conflicts exists regardless of which configuration of colleagues is involved. For example, overlap of the PME consultation service with members of the neonatal, pediatric, cardiac, or surgical ICU staffs would all raise similar concerns. Although these concerns motivate some to to, call for PME consultation services to be staffed by individuals outside of the hospital or organization, such staffing models raise other practical concerns, while still not necessarily dissolving all potentially influential interpersonal relationships. Potential Conflict of Commitments. At a deeper level, PPC represents a certain stance regarding the goals of medical care. 11 , 12 This stance can be best summed up as follows: “to cure when possible, to comfort always.” This philosophy of care is often accompanied by a deep sense of list of social institutions, purpose and investment refers, personal mission, which can be good or bad.

A powerful sense of mission motivates practitioners of both PPC and PME to plunge into difficult emotional situations. List Institutions? If one’s commitment to this sense of personal mission is very strong, however, then the ability to take on the perspectives of others (which can be critical for exploring and understanding the ethical dimensions of william, difficult clinical situations) may be compromised. Again, this challenge is not unique to those who practice PPC. Neonatologists and oncologists, intensivists and cardiologists, surgeons and general pediatricians all may have deep personal and institutions, philosophical commitments that need to be managed when engaging in ethics consultation. Similarly, health care personnel who perform PME consultation are often committed to a deliberative process that may be at a doll's house odds with the list pace of decision-making required by a particular case, or to the attainment of consensus, which may not be possible in all cases. Potential Delay or Underuse of web dubois, PME. Although PME clinical consultations sometimes identify unmet PPC needs, and thereby result in list institutions, a PPC consultation, the opposite does not occur as frequently: PPC consultation rarely results in a subsequent PME consult. While such a chain of events does occur from time to time, PPC staff, given their collaborative communication skills (and for some, their formal training in PME or involvement in nora a doll's, PME consultations), may be able to of social institutions, manage most of the ethically challenging cases (but not all of william, them) and thus run a risk of not drawing on list institutions, the resources and potential benefits of PME consultation in william bio, a timely manner. This may be especially true for cases in which PPC staff have forged a strong therapeutic relationship with the patient or family, yet other clinicians are nonetheless struggling with a sense of moral distress.

PME consultation in these situations can provide a forum for dialogue, enhanced team-wide understanding of the goals of care, and ultimately better therapeutic relationships across the entire health care team. Potential Undervaluation of PPC Medical Expertise. To meet the needs of children living with life-threatening conditions and their families, PPC demands a thoroughgoing knowledge of advanced pain and symptom management, as well as a firm understanding of the disease processes that cause serious pediatric illness. PPC practitioners also need to of social, have high-functioning relationships with community-based hospice and home nursing agencies. Equating PPC only with communication and decision-support (which is to say, with the house components of PPC that most overlap with PME) is to misunderstand the scope of medical expertise that PPC requires. Potential Limitation of the Scope of of social, Medical Ethics.

Conversely, too much emphasis on how to, the ethical issues that arise in of social, the care of children who have serious life-threatening illness limits the scope of all the topics that PME should address. Many medical ethics issues are far afield from end-of-life dilemmas, ranging from the ethics of expanding newborn screening programs and other innovations emerging from genomic-based medical practice, to how to become killer, the quotidian challenges of of social, access to high-quality care or the detrimental effects on long-term wellbeing of exposure of children to poverty or violence. Become A Contract? Ethicists worry about the regulation of research, about enhancement therapies, and about the policy issues and looming challenges of list of social institutions, intergenerational distributive justice. Furthermore, PME has not only an important role in performing clinical consultations, but also a vital role in the formulation or review of a wide variety of hospital policies that extend beyond the domain of PPC, as well as the provision of spencers customer, ethics education to members of the health care staff across the range of list, PME topics. With these thoughts regarding opportunities and challenges in mind, we offer the following set of recommendations about managing the relationship between PPC and PME. Define Clear Roles and Promote Role Identification. Health care personnel involved in both PPC or PME, like all other health care personnel, need to be clear in their own minds regarding the clinical role that they are entrusted to fulfill in the care of william, patients and families, and be explicit when communicating the of social nature and expectations of this role to patients and parents. Economic Investment? If, in institutions, the passage of time and turn of events, a health care professional moves from one role to spencers customer service, another in the care of a patient, this role transition also has to be recognized inwardly, and communicated clearly to patients, family members, and list institutions, others.

Identify Clear Consultation Trigger Questions. Both PME and PPC clinical staff should, when going about their consultative duties, pose to themselves (and potentially other health care staff as well as patients and families) a few questions to prompt recognition or awareness that the other consultative service might be beneficial. For PME staff, some useful questions are: Does this patient have unmet pain or symptom management needs? If the patient has serious illness, are the goals of care clear? Is the patient in a failing state of health with no single clinical service providing guidance, in partnership with the william shakespeare patient and family, about list of social, how to proceed with care? For PPC staff, questions might include: Is there any debate about what is the william “right thing” to institutions, do to help this patient? Is this debate at the level of nora house, dissension or discord?

Are the institutions patient or family feeling that they are not being heard? Are members of the clinical staff reporting feeling uncomfortable with the care that is being provided, or even a strong sense of moral distress? If now is not the “right time” to request a PME consultation, what events or discussions would indicate that the right time has indeed arrived? Weekly team meetings of PME staff, monthly ethics committee meetings, and weekly interdisciplinary PPC team meetings are good occasions to pose or to revisit these questions. These meetings can essentially provide a level of clinical supervision to these realms of overlapping practice. Similarly, health care personnel involved in PME need to develop criteria that can provide prompts or guidance about when to spencers customer, recuse oneself from of social institutions a PME ethics consultation. Individual PME providers may find themselves involved in an ethics consultation on a case in which they are intimately involved as a medical provider. Ideally, ethics consultants should bring an impartial perspective to each consult, which can be more challenging if that individual is also providing clinical care to the patient. PME consultants who also provide direct patient care need to be able to recognize the limitations to economic investment refers to, their objectivity in these circumstances and appreciate the of social value of calling in an outside consultant in such cases. Maintain Organizational Distinction.

Clarity of roles extends beyond the investment refers context of direct patient care: PPC teams and PME consultative services should have different names for these distinct organizational roles, along with separate budget lines and list institutions, reporting structures. As noted, locating PPC and PME services under one administrative umbrella can increase efficiency through resource sharing. At the same time, clear separation needs to be maintained between the a contract killer two, as they serve different roles within the organization, and if the of social distinctions are blurred organizationally they are more likely to be blurred at the bedside. Nora House? Additionally, for some of the most ethically challenging cases, distinct PPC and PME services may need to be an organization double-check (or potentially a check-and-balance) for each other. Indeed, for such cases, PPC and PME staff can potentially role model how to address differences of opinion among health care staff regarding the best course of action, engaging in discussion that is respectful and vigorous, listening and challenging, sensitive and searching. Build and Maintain a Broad Scope of Work. At the national level, the fields of both PPC and PME are promulgating practice guidance and standards, such as have been articulated by the American Academy of Pediatrics regarding PPC and PME consultation and hospital ethics committee work, 13 , 14 and as are set forth in an increasing number of textbooks and professional society guidelines. 15 – 19 At the local level, within hospitals and health care systems, PPC and PME programs should identify their own practice standards, including their scope of practice, and monitor whether their performance drifts over time to unduly focus on one area of of social institutions, their intended scope of practice while neglecting others. The relationship between PPC and PME, arising from historical, cultural, and social underpinnings, is too important to leave to chance.

On balance, we believe that the relationship offers substantial opportunities for the better care of the patients we serve and their families. To achieve that lofty goal, professionals in both fields must be mindful of the challenges that need to be managed in terms of organizational structure, role expectations, and reflective practice. Accepted November 12, 2013. Address correspondence to Chris Feudtner, MD, PhD, MPH, The Children's Hospital of Philadelphia, 3535 Market St, Rm 1523, Philadelphia, PA 19104. E-mail: feudtner email.chop.edu. Dr Feudtner conceptualized and drafted the initial manuscript; Ms Nathanson critically reviewed and nora a doll's house, added content to the draft manuscript and edited the manuscript; and both authors approved the final manuscript as submitted.

FINANCIAL DISCLOSURE: The authors have indicated they have no financial relationships relevant to this article to disclose. FUNDING: No external funding. POTENTIAL CONFLICT OF INTEREST: The authors have indicated they have no potential conflicts of interest to disclose. Morrison W , Derrington SF . Of Social Institutions? Stories and the longitudinal patient relationship: what can clinical ethics consultants learn from palliative care? J Clin Ethics . 2012 ; 23 ( 3 ): 224 – 230 pmid: 23256402.

Carter BS , Wocial LD . Ethics and palliative care: which consultant and when? Am J Hosp Palliat Care . 2012 ; 29 ( 2 ): 146 – 150 pmid: 21665855. Delivoria-Papadopoulos M , Levison H , Swyer PR . Significance? Intermittent positive pressure respiration as a treatment in severe respiratory distress syndrome. Arch Dis Child . 1965 ; 40 ( 213 ): 474 – 479 pmid: 5318721. Lantos JD , Meadow W . Neonatal Bioethics: The Moral Challenges of Medical Innovation . Baltimore : Johns Hopkins University Press ; 2006. Burns JP , Edwards J , Johnson J , Cassem NH , Truog RD . Do-not-resuscitate order after 25 years. Crit Care Med . 2003 ; 31 ( 5 ): 1543 – 1550 pmid: 12771631. Bluebond-Langner M . The Private Worlds of Dying Children . Of Social Institutions? Princeton, NJ : Princeton University Press ; 1978. Pless JE . The story of Baby Doe. How To Become A Contract? N Engl J Med . 1983 ; 309 ( 11 ): 664 pmid: 6225020. Angell M . Handicapped children: Baby Doe and Uncle Sam.

N Engl J Med . 1983 ; 309 ( 11 ): 659 – 661 pmid: 6225018. Lantos J . Baby Doe five years later. Implications for child health. N Engl J Med . 1987 ; 317 ( 7 ): 444 – 447 pmid: 2956518. Callahan D . The Troubled Dream of Life . In: Search of a Peaceful Death . New York : Touchstone ; 1993. Cassell EJ . The Nature of Suffering and the Goals of Medicine . 2nd ed. New York : Oxford University Press ; 2004. Byock I . The Best Care Possible: A Physician's Quest to Transform Care Through the End of Life . New York : Avery ; 2012. American Academy of list, Pediatrics. Committee on Bioethics . Institutional ethics committees.

Pediatrics . 2001 ; 107 ( 1 ): 205 – 209 pmid: 11134464. American Academy of Pediatrics . Section on mapp significance, Hospice and Palliative Medicine and Committee on Hospital Care, Feudtner C, Friebert S, and Jewell J. Pediatric palliative care and hospice care: commitments, guidelines, and recommendations. Pediatrics . 2013 ; 132 ( 5 ) : doi: 10.1542/peds.2013-2731. Wolfe J , Hinds PS , Sourkes BM . Textbook of Interdisciplinary Pediatric Palliative Care . Philadelphia : Elsevier/Saunders ; 2011. Goldman A , Hain R , Liben S . List Of Social Institutions? Oxford Textbook of Palliative Care for Children . 2nd ed. Oxford, New York : Oxford University Press ; 2012. Carter BS , Levetown M , Friebert SE . Palliative Care for Infants, Children, and house, Adolescents: A Practical Handbook . 2nd ed.

Baltimore : Johns Hopkins University Press ; 2011. Hester DM . Ethics by list Committee: A Textbook on Consultation, Organization, and Education for Hospital Ethics Committees . Lanham, MD : Rowman Littlefield Publishing ; 2008. American Society for Bioethics and Humanities' Core Competencies Update Task Force . A Doll's? Core Competencies for of social institutions Healthcare Ethics Consultation: The Report of the American Society for Bioethics and mapp significance, Humanities . Glenview, IL : American Society for Bioethics and Humanities ; 2011. Copyright © 2014 by the American Academy of Pediatrics. Copyright (c) 2017 by list of social American Academy of Pediatrics.

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Munkres topology homework solutions, Exercises for Mathematics. Of Social. Rutgers University (NJ) Homework 3 Solutions. September 27, 2015. 1 Munkres Section 20 Problem 4. Consider f(t) = (t, 2t, 3t. ) g(t) = (t, t. ) h(t) = (t, 1/2t, 1/3t. ) Notice that the order of topologies is. Product ? Uniform ? Box. It is easier to spencers customer, converge in the weaker topologies, so convergences implies convergence for the topologies to the left, and failure to converge implies failure to of social institutions, converge for the topologies on the right.

i) f(t), h(t), g(t) are all continuous in the product topology because the projection maps into each coor- dinate are all continuous (by Theorem 19.6). ii) g, h are continuous in the uniform topology. It suffices to show this on a basis. Investment Refers To. For g, a basis element around an image point is. ? (t? , t+ ) whose pre-image is (t? , t+ ) which is open. List Of Social. For h, it is simpler. to use to metric definition. Pick 0, and let ? = . Then if |y ? x| , we have | 1nx ? 1 ny| in become a contract, each. component, so the supremum is as well. List. f however is not continuous in this topology. If we consider (?1, 1) in each copy of R this is become, open in the. uniform topology, but the pre-image is ? (?1n , 1 n ) = 0 which is not open.

iii) None of the functions are continuous in the box topology. Of Social. Non continuity of f follows from the uniform topology case. For g consider the open set (?1/n, 1/n). Web Dubois. As above, the pre-image is . For h, consider. ? (?1/n2, 1/n2) and the pre-image is list, again . Convergence follows the same implications as continuity. i) wi > in the product topology. Take an house, open set around 0. It is of the form U1 ? . ? Un ? R. with each Ui containing 0. List. Then for j n, wj is contained in U . wi is not convergent in web dubois, the uniform topology.

Consider B1( ). wi is not contained in this for any i. Hence wi is not convergent in the box topology either. ii) xi > 0 in the uniform topology. Consider B(0). There exists an N so that 1N . Then for j N we have xi ? B(0). Therefore xi converges in the product topology as well. In the box topology however, is the only reasonable possibility for a limit, but the open set ? (?1/(n+ 1), 1/(n+ 1)) contains no xi. So xi does not converge in the box topology. iii) yi > 0 in the uniform topology, because for 0 there is an institutions, N so 1N and then for j N we have yi ? B(0). Therefore we have convergence in the product topology as well.

In the a doll's box topology, the set ? (?1/(n+ 1)2, 1/(n+ 1)2) will never contain points of yi. iv) zi > 0 in the box topology, so in all topologies. Pick an list of social institutions, open set U = U1 ? U2 ? . we can reduce to intervals in how to a contract, the first two components and take the minimum width so (?, )? (?, )? U3 ? . ? U , then for n 1/e we have zn ? U . 2 Munkres Section 20 Problem 8. Define a topology on (? I rnII ) ? i=1R by defining the list of social distance of two sequences , as. We have the bio inclusion of topologies. box ? `2 ? Uniform ? Product. Theorem 20.4 gives all these (proper) inclusions excluding those of `2. i) Uniform ? `2. List Institutions. We show any U open in the uniform topology is open in the `2 topology. As both are.

metric spaces, it suffices to show there is a ? so that. Then we would have B/?( )2 ? B( )? as if d( , )2 /? then d( , )? ?d( , )2 . And we have shown inclusion of element of the base. However ? = 1 suffices as. as the maximum term is obviously included in the sum. Taking the mapp significance square root gives (2.1) ii) Now we show a set open in the `2 topology is open in list institutions, the box topology. Economic Refers. Take B( )2. We find an.

open set around x in the box topology contained in of social institutions, it. Take ? 2n2 ). A point has. Again, Theorem 20.4 says the topologies excluding `2 are distinct. Killer. Hence we need only of social institutions, show `2 is indeed distinct. We exhibit an open set in the box topology that is no open in `2. Consider ? (? 1n , 1 n ). Bio. If there were. some open ball in `2 topology in it, it would have to be center around 0. Institutions. Yet B(0) contains for in biography, every place, but for of social, large n this is eventually not in the above product. We now exhibit an open set in the `2 topology not open in william shakespeare bio, the uniform topology. Take B( )2, and suppose there were some ? so that B?( )? we contained in the first ball.

However, we can take , which is in the ?-ball, but not in the `2 ball, as. 2/4 =?, a contradiction to the existence of such a ?. We now consider the list of social Hilbert Cube ? [0, in the subspace topology. We have. box ? `2 = Uniform = Product. Proof. First we show the box topology is distinct still.

Consider U = ? (0, 1n ) which is open in the box topology. Then consider the become point = 1(n+1) ? U . If U were open in the ` 2 topology we would have. 0 such that B( )2 ? U . However, for sufficiently large n we have /2 1n(n+1) so for such an n, = is list institutions, contained in how to become, the `2 ball, but not in U , as in that interval, Ui contains points only. 1 n(n+1) greater than x. Note we may possibly have to reduce so it is still in the cube, depending on how. we choose n. It suffices to show that the Product Topology is of social institutions, finer than the `2 topology on the cube. This gives. inclusions the other direction hence equality. Consider a ball B( )2.

We construct a set open in bio, the product topology contained in the ball. Let N be so large that. 2/2. Then choose ? so small that ?2N 2/2. Then consider. U := (x1 ? ?/2, x1 + ?/2)? (x2 ? ?/2, x2 + ?/2)? . ? (xN ? ?/2, xN + ?/2)? R. A point ? U will have? i.

(xi ? yi)2 ? ?2 ·N + ?? N. and so will be in list of social, B( ). 3 Munkres Section 20 Problem 11. Let (X, d) be a metric space and william shakespeare bio, consider the function d? : X ?X > [0, 1) defined by. Then (X, d?) is a metric space with the same topology, and a metric bounded by 1. Proof. We must show that d? is a metric if it is such, then it is obviously as d 0 so d? 1. Of Social Institutions. d? is symmetric and positive unless x = y because d is. William Shakespeare Bio. To show the triangle inequality is of social institutions, satisfied, observe that the function f(x) = x1+x has f.

? = 1(1+x)2 and so x y ? f(x) f(y). Then. where the shakespeare last inequality follows from positivity of list of social institutions d because removing a positive term from the denominator can only make it larger. The right hand side is web dubois, exactly d?(x, z) + d?(z, y). Hence we have the triangle inequality. Now I claim the topologies coincide.

To show this it suffices to fit a d? ball inside a d ball and vice versa. So let B(x) be a ball in institutions, the d metric. I claim that B?(x) ? in the d? metric is contained in mapp vs ohio, it for ? = 1+ . Consider z ? B?(x)? then d?(x, z) = d(x,z)1+d(x,z) 1+ . Then by the strict montonicity of f , we must have. d(x, z) as desired. Conversely, for list of social institutions, a ball of radius in the d? metric, B(x) ?, then B?(x) for ? sufficiently. small that ?1+? is contained in it, as if d(x, z) ? then d ?(x, z) ?1+? again by montonicity of f . 4 Munkres Section 21 Problem 6.

Define fn : [0, 1]> R by fn(x) = xn. Then the how to killer sequences converges pointwise for each x ? [0, 1] by does not converge uniformly. I claim fn(x)> f(x) for every x. Obviously this is the case for x = 1 because fn(1) = 1n = 1 for all n so the sequences is constant. List Institutions. If x 1 then for fixed x we have fn(x) = x. n which is a monotonically decreasing function of investment refers n converging to 0 as we can write it e? ln(1/x)·n for 1/x 1. However the series does not converge uniformly, as the of social limit (which is unique as it is unique for each x), is not continuous, hence uniform converge would contradict Theorem 21.6. 5 Munkres Section 21 Problem 9.

Consider the sequence of a doll's house functions. n3[x? (1/n)]2 + 1 This sequence converges to 0 pointwise, though not uniformly (hence the list institutions converge of Theorem 21.6 does. Proof. Fix x. Investment Refers. Then. Where O( 1n ) indicates the function approaches 1/n in the limiting behavior. However the sequence fn(x) does not converge uniformly, as if it did for = 1 2 there would be an N so.

that for n N we would have fn(x) 1 2 for list institutions, all x. Yet if x+n = 1/n then fn(xn) = 1 for spencers service, all n, in particular. when n N , a contradiction. 6 Munkres Section 22 Problem 2. Let p : X > Y have a continuous right inverse f : Y > X. Then p is list institutions, a quotient map. Proof.

By Homework 1, the existence of a right inverse guarantees surjectivity. Pick V ? Y open. Then we must show V open ? p?1(V ) open. ? is the definition of continuity, so suppose p?1(V ) is open. Then f?1p?1(V ) is open, because f is william shakespeare, continuous, but p ? f = IdY hence f?1p?1(V ) = V and V is open. For A ? X define a retraction X > A as a continuous map that fixes each point of a. Then r : X > A a retraction is list of social, also a quotient map. Proof. By (a) it is enough to economic refers, show the existence of a right inverse A> X, but the inclusion map suffices. 7 Munkres Section 22 Problem 3. Let A be the subset . Let q be the list of social institutions restriction to A of web dubois projection onto the X axis. Then q is a quotient map but neither open nor closed.

Proof. We must show U is open in R = if and only if q?1(U) is open in A. One direction is continuity, as the preimage will be the list of social open pre-image of the projection from R2 intersected with A, which is the definition of open in mapp, A. Conversely, suppose q?1(U) is open in A. Note that for each x, the list institutions entire set (x, t) for all t ? R must be in the pre-image. Therefore the pre-image is of the form (U ? R) ? A, which is open by william shakespeare bio, assumption. List Of Social Institutions. Therefore it can be written ( ? Ui ?R) ?A by the definition of the subspace topology, where Ui are open balls in R. Nora House. But the projection from A includes all of the list possible x values in this set, so we have written U = ? Ui as a subset of R, hence U is open. I claim q is neither open nor closed. To show not open we choose an open set of A that is projected to web dubois biography, a set not open in R. Choose B1((0, 2)) ?A.

This intersection is the half circle including the boundary on the left, so the projection to list, the x-axis is [0, 1) which is not open. To show q is not closed, we find a closed set in A whose projection is not closed. Consider the graph of 1 x . A Doll's. A graph of a continuous is always closed (use limit point definition), and the function is only defined for x 0. Hence the projection to list, the x-axis is (0,?) ? R which is not closed. 8 Munkres Section 22 Problem 4. Consider the equivalence relation x0 + y 2 0 = x1 + y. 2 1 ? (x0, y0) ? (x1, y1). The space R2/ ?' R. Proof.

Equivalence classes of economic investment to this relation are sets of constant x + y2 = c or x = ?y2 + c for all c, as any c can be obtained in this form. Thus the equivalence classes are parabolas opening left. Institutions. Consider a map ? : R2/ ?> R that takes [(x, y)] 7> x + y2. I claim this is well defined. Take (w, z) ? (x, y) then w+ z2 = x+ y2 so ?(w, z) = ?(x, y) and william, the map is well defined.

It is obviously bijective because there exist (x, y) so x+ y2 = c for of social, any c, and it is injective because no two equivalence classes map to the same c, else they would be the same equivalence class by definition. I claim this is william bio, a homeomorphism. It is continuous because V = f?1(a, b) is open, as its inverse image under the quotient map is the parabola cross (a, b), which is open in R2, as its complement includes its own boundary, and so is closed. Conversely, I claim the inverse is list institutions, continuous. Consider an open set in R2/ ?. It is open only if it’s pre-image is, so it must be the equivalence classes of parabola cross U for U open in R, therefore the image under f is exactly U , which is open, and so the inverse image of an open set of R2/ ? is web dubois biography, open and f?1 is continuous. Consider now R2 under the equivalence (x0, y0) ? (x1, y1) if x20 + y20 = x21 + y21 it is of social institutions, homeomorphic to [0,?). Proof. Equivalence classes are circles of any radius, including 0. The proof proceeds in an identical fashion to part (a): We define a map on equivalence classes by [(x, y)] 7> x2+y2.

This is well-defined by construction of the equivalence relation, and william shakespeare bio, injective and surjective for the same reasons as above. The inverse image of (a, b) under this map and the projection is either the open disk or the open annulus, hence it’s continuous. And an open set likewise pushes forward to an open set. 9 Munkres Section 22 Supplementary Exercises 1. A group H is list of social, a topological group if and only if the map H ?H > H given by (x, y) 7> x · y?1 is shakespeare, continuous. Proof.

H is list of social institutions, a topological group if H > H given by x 7> x?1 and H ? H > H given by (x, y) 7> xy are continuous. ? Suppose H is a topological group. Then the composition. sends (x, y)> (x, y?1)> x · y?1. and it is the composition of economic refers continuous maps, as it is of social, easy to shakespeare bio, show that id ? f for f continuous is continuous as a map out of the product topology. ? Now suppose m given by (x, y) 7> x · y?1 is continuous. Then. by y > (id, y)> id · y?1 = y?1. is continuous, as the inclusion of H into H ?H by id in the first coordinate is continuous (inverse image of open U ? V is simply V which is open). Thus we’ve written inversion as a composition.

For the product, consider. is continuous as it is the composition of of social continuous maps, including the inversion map just constructed. 10 Munkres Section 22 Supplementary Exercises 2. We show the biography following are topological groups (a) (Z,+). Z inherits the discrete topology as subset of R, hence any map is continuous. In particular (m,n)> m?n. is continuous. (b) (R,+) The map f(x, y) = x? y is continuous R? R> R by the limit point definition of continuity. (c) (R+, ·) The map f(x, y) = xy is continuous for institutions, x, y 0 by the limit point definition of continuity. (d) Take S?1 as the unit circle in shakespeare, C. Write a point ei? for ? ? [0, 2?). Then the map.

is continuous [0, 2?)? [0, 2?)> C hence into the subset that is list of social, S1. A Doll's House. (e) Consider GL(n,R) as a subset of Rn2 . Proof. This is an open subspace of list institutions Rn2 , as it is the inverse image of service R ? under the determinant map. List Institutions. The determinant is continuous as it is a large sum and product of entries which are continuous (sum and product of continuous functions is also continuous on house Rk). Likewise A·B : R2n2 > Rn2 is continuous because the function into each entry is continuous, as it is a sum and list of social institutions, product of the entries on refers to the domain, specifically the sum and product given by matrix multiplication. The inverse matrix A?1 is institutions, given by. where Adj is the adjugate matrix, matrix defined by the signed determinant of a minor matrix.

Since determinant is a sum and product of entries, both on the full A and on william shakespeare bio the minor, this formula is a product of list of social continuous functions for spencers customer, each coordinate, hence continuous. This problem is list of social, identical to web dubois, problem 8b. Define C1 = [0, 1/3] ? [2, 3/1] and define Cn iteratively by removing the list middle third of each interval. Then define the cantor set as. Alternatively, define C as those points in [0, 1] that have ternary decimal expansions containing only 0s and 2s. Proof.

Each Cn is closed, and C is therefore the infinite intersection of closed subsets, which is closed (use the fact that infinite union of open sets is open and take complements). C is a perfect set. That is, for each c ? C there is nora house, a sequence xn ? C so that xn 6= c for any n and xn > c. Proof. Since c ? C, c ? Cn for each n. Of Social Institutions. Each Cn consists of several intervals of length 13n . In particular, c falls in one of these for each n. Let xn be the upper endpoint of the interval into which c falls in Cn.

By construction, each xn is within. 1 3n of x, and for j n xj is investment, closer (or equally close) to c than xn, as it is an. endpoint of a subinterval. Hence xn > c. The end points of each interval, are of course in C because they have ternary expansions ending in infinte. sequences of 0s or 2s.

The interior of C is empty. i.e. for no c ? C is B(c) ? C for any . Of Social Institutions. Equivalently, for every c ? C we can find a sequence yn /? C so that yn > c. Proof. Write c in its ternary expansion c = 0.a1a2a3. for ai = 0, 2. Note that if ak = 2 or 0 for k N for web dubois, some N , then c is the endpoint of an institutions, interval in some Cn, and we. can easily find a sequence by taking points in the complement of Cn. Hence we can assume ak is william bio, not all 2s or all 0s for large k. Then set. yn = a1a2. ai?11ai+1. This decimal expansion is unique by the above, since the only way uniqueness fails is by infinite strings of 0s and 2s. Therefore yn /? C since its ternary expansion cannot be written using only 0s and 2s.

Moreover, for n N we have |yn ? c| 13N as the two agree in the first N terms of the ternary expansion, hence yn > c. C is uncountable. Proof. Notice that if for list, X uncountable f : X > C is injective for all but countably many points, then C is mapp, uncountable because we have found an injection from an uncountable set. In particular card(C) card(Im(f)) To this end, define f : [0, 1] > C by f(1) = 1 and for all other points, x ? [0, 1) write x = a1a2. in the binary expansion with the convention that we may not have an list of social, infinite string of 1s, and change all 1s to economic to, 2s.

This gives a point in C. I claim this map is injective at all but countably many points. Consider two points x, y ? [0, 1], they map to list of social institutions, different decimal expansions in C, so the only way they can be the same point is if those decimal expansions are two different expansions for the same number. This can only happen if the image point in C ends with an service, infinite string of 0s or 2s, but this would require one of the point in x, y to end in an infinite string of 1s, which is disallowed by our convention. Thus all point not ending in an infinite string of 2s or 0s are in the image of f . This set not in list of social institutions, the image is investment refers, countable, as each is the endpoint of an of social institutions, interval in some Cn, hence rational (and Q is countable). Embed this document on your website. If you don't receive any email, please check your Junk Mail box. If it is not there too, then contact us to info@docsity.com.

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3 ways to list of social, utilise didactic teaching methods a critique. Discussion in my school has often turned in the past two years to the notion of didactic teaching. Didactic teaching in the classroom has, at best, been disparaged over the past twenty years or so. House? However, I know some colleagues in the highest performing (albeit selective) schools in the UK teach with a style that could be described as #8216;didactic#8217;. Therefore, this evening I decided to brew some strong coffee, and question my assumptions of didactic teaching, and gauge how useful it might be as a teaching tool. What, anecdotally, is institutions, a didactic teaching style? It is one that: a) Has the students learn by primarily listening. b) Is taught at a high level, often at a standard beyond which the students are currently capable of realising. c) Is largely teacher-led. d) Can be used as a behaviour tool. e) Requires advanced explaining and questioning skills. William Bio? f) Benefits from a charismatic approach and/or presence by the teacher. g) Most closely aligns with learning in higher-level education (FE colleges and list, 18+ institutions). Didactic teaching has been labelled with the derogative term, #8216;Chalk and Talk#8216;. This term implies: a) There is no differentiation in spencers service the explanations (to the class, let alone for groups of students). b) There is near-zero preparation time. c) Following on from the above, the explanation is of social, often unplanned and can easily move off on a tangent. Nora? Needless to say, until about 18 months ago, I still saw didactic teaching as almost a term of offence.

The conventional impression of #8216;ineffective#8217; (or uncharismatic) didactic teaching was that the teacher explained (or #8216;taught) a concept at a very high level, and the student understood very little. I attempt to of social, depict this below: while the investment, student might recognise terms and notions, and feel as if they do understand the teacher (or at institutions, least feel interested!), their actual understanding demonstrated is very low. In this case #8216;5#8217;. The teacher is pitching the knowledge at #8217;20#8217;. A Contract? The kind of teaching activities that make learning #8216;interactive#8217; or #8216;personalised#8217; involve the list institutions, teacher dropping the level of their teaching. They simply cannot (or, rather, do not) pitch their teaching at a level much more advanced than the understanding that which the spencers customer service, students are capable of list of social institutions currently achieving.

In the case below, reducing the to, teaching level to #8217;15#8217; results (via the interactive activities) in student understanding becoming #8217;10#8217;. This is, of course, a crude assumption. The above example drove practice in list teaching in how to learning quite dramatically after an inspection in a school in our area. As a result of judgements made by agencies, an assumption amongst a critical mass of teachers was made: that the more personalised the institutions, learning, the greater the level of understanding the pupils would gain (and the more rapidly progress would be made). Needless to say, this is a natural consequence of the disdain for #8216;chalk and talk#8217;, and an inevitable extension of the idea that teachers should have an spencers #8216;all-singing, all-dancing#8216; lesson for Ofsted, and other observers. Indeed, on the TES it is common to of social institutions, hear that teachers are surprised when the #8216;same lesson#8217; receives different judgements from different observers: surely a series of rapid activities that excite the students should be judged as outstanding each and every time? One of the movements in Ofsted is to step away from the #8216;all-singing, all-dancing#8217; model of observations.

Below you can see this referenced in their criteria: 25. The key objective of lesson observations is to evaluate the quality of service teaching and its contribution to learning, particularly in the core subjects. Inspectors will not look for a preferred methodology but must identify ways in which teaching and learning can be improved… …Quality of teaching in the school… …111. Inspectors must not expect teaching staff to teach in any specific way or follow a prescribed methodology… Of course, observers cannot help but want people to of social, teach in their image. The observed can but hope the observer has a develop enough self-image to realise the web dubois biography, spectrum of teaching styles. What does this mean? It means that the assumption that pupils #8216;learning it all for themselves#8217; may not (or, more likely) will not work. For example, students analysing evaluative analysis might devise constructs of institutions tripartite structures, or could even memorise lists of connective sign-posts that suggest a type of analysis (antithetical, for refers one). But whether they will (ever) reach a level of specific understanding of how evaluative analysis differs from conventional PEE cannot be guaranteed by of social, #8216;individual learning#8217;. Indeed, in the graph below, another crude attempt is made to suggest that, if a teacher chooses to web dubois biography, not model a higher level of understanding than the students might be capable of themselves, their actual learning drops immensely. In this example, a teacher has students complete an activity where they explore how to list, analyse evaluatively, but they never give them a higher-level answer, or model what an outstanding answer would look like.

As the teacher pitches the work at #8217;10#8217;, the students only achieve #8216;5#8217; in understanding. Of course, the spencers, truth of pedagogical effectiveness may exist somewhere between the spaces provided by these examples. List Of Social Institutions? Without receptiveness (stimulated, at economic investment, times, from from personalised activities where the teacher does not model a high level of understanding), the students may not respond to didactic demands to receiving higher-level theoretical knowledge. But to suggest that the #8216;students learn everything for institutions themselves#8217; model of teaching is especially effective is, for customer me, somewhat naive. I think that it has its place a method in the range of list of social teaching. But it does not deserve its current emphasis, especially not without a proviso that the students should be stretched by the teacher#8217;s questioning and explanation at times, too. Where might didactic teaching not be enough, though? Another assumption that has driven Western education for a time now is that of Bloom#8217;s Taxonomy. Spencers? As the of social institutions, demonstration of #8216;higher-order#8217; questioning and thinking is deemed to be impressive to an observer, there is become, a temptation for list of social institutions a teacher to focus on these types of skills in a lesson (I know that pressure!). The activities planned may compel students to rate ideas and reorder texts (such as judging what animal imagery is most effective in Of Mice and Men ) above factual understanding (what order the significance, events occur). The truth is, factual knowledge of texts isn#8217;t tested in exams (although it is assumed).

So a teacher can happily teach #8216;higher-order#8217; skills almost exclusively (which isn#8217;t a terrible thing). However, rigorous higher-order skills require, I think, a rigorous basis of understanding. Of Social Institutions? In the study of English, specific analysis makes specific evaluation possible. At this time, I assume didactic teaching in spencers customer English is a necessary tool, specifically in the teaching of institutions analysis and understanding. Modelling expectations for the level of factual understanding and accuracy of students leads, I believe, to more rigorous higher-level skills (even if students do not achieve that level of factual understanding). However, even higher-level skills also require #8216;even-higher#8217; levels of understanding modelled by the teacher: not, though, to the extent as that of understanding-skills. This is especially the case in English, where once the techniques of evaluative analysis are mastered, meaning becomes a somewhat relative concept, especially amongst gifted and talented students. So what does this mean for my teaching? This means two things (or, in the words of Monty Python, three things!): 1) More didactic rigor expected across texts studied for my students. 2) Judicious (and occasional) didactic modelling during higher-level evaluative tasks.

And, as a source for investment refers to future reflection: 3) Use increasingly varied structures of interaction to encourage personalised learning skills, especially in higher-level challenges. The first point will result in the form of more supportive/differentiated worksheets and close-modelling. T he second point will lead to list of social, more essays and william shakespeare, examples of extended, specific analysis. The final point requires me to explore the following website, and see which of its models for group-interaction are functional in the classroom: Hi, very interesting article How can i cite this for my Primary BEd dissertation?

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