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Paperback. Zustand: New. 2010 ed. These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we ?nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC? We will consider quite classical properties of Banach spaces, such as "- ing re?exive," "having separable dual," "not containing an isomorphic copy of c ," "being non-universal," etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is "simple." The "simplicity" ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural "coding" of separable Banach spaces, then we can indeed ?nd a separable space Y which is universal for the class C and satis?es the requirements imposed above. …

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC We will consider quite classical properties of Banach spaces, such as '- ing re exive,' 'having separable dual,' 'not containing an isomorphic copy of c ,' 'being non-universal,' etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is 'simple.' The 'simplicity' ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural 'coding' of separable Banach spaces, then we can indeed nd a separable space Y which is universal for the class C and satis es the requirements imposed above. …

Paperback. Zustand: New. 2010 ed. These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we ?nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC? We will consider quite classical properties of Banach spaces, such as "- ing re?exive," "having separable dual," "not containing an isomorphic copy of c ," "being non-universal," etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is "simple." The "simplicity" ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural "coding" of separable Banach spaces, then we can indeed ?nd a separable space Y which is universal for the class C and satis?es the requirements imposed above. …

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Hardback. Zustand: New. Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics.This book is devoted to one of the most important areas of Ramsey theory-the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemeredi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem.This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.…

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Hardback. Zustand: New. Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics.This book is devoted to one of the most important areas of Ramsey theory-the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemeredi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem.This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.…

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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -These notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution relies heavily on techniques coming from Descriptive Set Theory. Thecentralthemeisuniversalityproblems.Inparticular,thetextprovides an exposition of the methods developed recently in order to treat questions of the following type: (Q) LetC be a class of separable Banach spaces such that every space X in the classC has a certain property, say property (P). When can we nd a separable Banach space Y which has property (P) and contains an isomorphic copy of every member ofC We will consider quite classical properties of Banach spaces, such as '- ing re exive,' 'having separable dual,' 'not containing an isomorphic copy of c ,' 'being non-universal,' etc. 0 It turns out that a positive answer to problem (Q), for any of the above mentioned properties, is possible if (and essentially only if) the classC is 'simple.' The 'simplicity' ofC is measured in set theoretic terms. Precisely, if the classC is analytic in a natural 'coding' of separable Banach spaces, then we can indeed nd a separable space Y which is universal for the class C and satis es the requirements imposed above. 168 pp. Englisch.…

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Kartoniert / Broschiert. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. - author has been a central player in new developments of this area- This book is a much needed expositionThese notes are devoted to the study of some classical problems in the Geometry of Banach spaces. The novelty lies in the fact that their solution .…