Cellular Structures in Topology

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Cambridge University Press, Sep 27, 1990 - Mathematics - 326 pages
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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.
  

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Contents

Adjunction of ncells
11
CWcomplexes
22
Subcomplexes
33
Finiteness and countability
40
Whitehead complexes
51
Combinatorial complexes
89
Simplicial sets
132
Spaces of the type of CAV complexes
223
Coverings
248
Union spaces of expanding sequences
273
Absolute neighbourhood retracts in the category of metric spaces
281
Dimension and embedding
299
Bibliography
306
List of symbols
313
Index
321
Copyright

Appendix
241

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About the author (1990)

Fritsch of the University of Munich, Germany

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