Cellular structures in topology. (English) Zbl 0837.55001

Cambridge Studies in Advanced Mathematics. 19. Cambridge etc.: Cambridge University Press. xi, 326 p. (1990).
Due to technical problems, the review of this book appears very late, but — hopefully — not too late. The text of the review was taken from the introduction. “Cellular structures play an essential role in topology, analysis and geometry; they appear in the form of CW-complexes, simplicial sets and so on. The idea of this book is to give a unified treatment of their fundamental geometric and topological (in the sense of general topology) properties. As a common basis for their representation we have chosen the CW-complexes. The first two chapters of this book are devoted to the theory of CW-complexes. Chapter 3 and 4 deal with the theory of simplicial complexes and simplicial sets; we feel that the existence of a very large body of research in that area and the importance of combinatorial structures in topology amply justify the relatively large size of these two chapters. In the fifth chapter we study the category of spaces having the homotopy type of CW-complexes. We end the book with an appendix containing the results of homotopy theory, topology and dimension theory necessary to the development of the book. Although most of the exercises can be worked out easily using the material in the text, there are some exercises which require the reader to consult the references given in each case”.


55-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology
55U10 Simplicial sets and complexes in algebraic topology
55P99 Homotopy theory