By
J. van Mill, Vrije Universiteit, Department of Mathematics and Computer Science, Amsterdam, The Netherlands
Description
The first part of this book is a text for graduate courses in topology. In chapters 1 - 5, part of the basic material of plane topology,
combinatorial topology, dimension theory and ANR theory is presented. For a student who will go on in geometric or algebraic topology
this material is a prerequisite for later work. Chapter 6 is an introduction to infinite-dimensional topology; it uses for the most part
geometric methods, and gets to spectacular results fairly quickly. The second part of this book, chapters 7 & 8, is part of geometric
topology and is meant for the more advanced mathematician interested in manifolds.
The text is self-contained for readers with a modest
knowledge of general topology and linear algebra; the necessary background material is collected in chapter 1, or developed as needed.
One can look upon this book as a complete and self-contained proof of Toruńczyk's Hilbert cube manifold characterization theorem:
a compact ANR X is a manifold modeled on the Hilbert cube if and only if X satisfies the disjoint-cells property. In the process
of proving this result several interesting and useful detours are made.
Included in series
North-Holland Mathematical Library
