Handbook of Algebraic Topology

Author: I.M. James

Publisher: Elsevier

ISBN: 9780080532981

Category: Mathematics

Page: 1324

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Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
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Handbook of the History of General Topology

Author: C.E. Aull,R. Lowen

Publisher: Springer Science & Business Media

ISBN: 9780792344797

Category: Mathematics

Page: 397

View: 7188

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This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
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Topological and Algebraic Structures in Fuzzy Sets

A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

Author: S.E. Rodabaugh,Erich Peter Klement

Publisher: Springer Science & Business Media

ISBN: 9401702314

Category: Mathematics

Page: 470

View: 2256

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This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.
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Handbook of K-Theory

Author: Eric Friedlander,Daniel R. Grayson

Publisher: Springer Science & Business Media

ISBN: 354023019X

Category: Mathematics

Page: 626

View: 3385

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This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
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Handbook of Mathematics

Author: Vialar Thierry

Publisher: BoD - Books on Demand

ISBN: 295519901X

Category:

Page: 1132

View: 7547

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The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
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Differential Algebras in Topology

Author: David Anik

Publisher: A K Peters, Ltd.

ISBN: 9781568810010

Category: Mathematics

Page: 274

View: 2422

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"We construct an infinite family ... of spaces that generalize the odd-dimensional Moore space ... Extending some work of Cohen, Moore, and Neisendorfer, we explore the homotopy-theoretic properties of these spaces and of several closely related spaces. In the process, we develop a variety of algebraic and geometric tools and techniques that may have wide applicability in unstable p-primary homotopy theory."--abstract.
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Handbook of Algebra

Author: N.A

Publisher: Elsevier

ISBN: 9780080532950

Category: Mathematics

Page: 912

View: 2747

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Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.
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Homotopy Type and Homology

Author: Hans J. Baues

Publisher: Oxford University Press

ISBN: 9780198514824

Category: Mathematics

Page: 489

View: 3569

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This book represents a new attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classification and includes applications to the classification of manifolds.
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