Cellular Structures in Topologyby Rudolf Fritsch, Renzo Piccinini
Pub. Date: 06/05/2008
Publisher: Cambridge University Press
The authors describe the construction and properties of CW-complexes. These spaces are important because they are the correct framework for homotopy theory, and most spaces that arise in pure mathematics are of this type. They discuss the foundations and also recent developments such as 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. The text clearly establishes the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises accompany each chapter ending with a section that sketches the historical development. An appendix gives basic results from topology, homology and homotopy theory.
Table of Contents
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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