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.
General
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