Cellular structures in topology
著者
書誌事項
Cellular structures in topology
（Cambridge studies in advanced mathematics, 19）
Cambridge University Press, 2008
- : pbk
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注記
"First published 1990. This digitally printed version 2008"--T.p. verso
"Paperback re-issue"--Back cover
Bibliography: p. [306]-311
Includes index
内容説明・目次
内容説明
This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.
目次
- 1. The fundamental properties of CW-complexes
- 2. Categories of CW-complexes
- 3. Polyhedra and simplicial complexes
- 4. Simplicial sets
- 5. Spaces of the homotopy type of a CW-complex
- Appendixes.
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