Infinite-Dimensional Topology

Prerequisites and Introduction

J. van Mill

• Publisher: North Holland
• Year: 1988
• Print ISBN: 9780444871336
• eBook ISBN: 9780080933689
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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 Toru?czyk'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.

Table of contents

• Front Cover
• Infinite-Dimensional Topology: Prerequisites and Introduction
• Copyright Page
• Table of Contents
• Preface
• How To Use This Book
• Chapter 1. Extension Theorems
• Chapter 2. Elementary Plane Topology
• Chapter 3. Elementary Combinatorial Techniques
• Chapter 4. Elementary Dimension Theory
• Chapter 5. Elementary ANR Theory
• Chapter 6. An Introduction to Infinite-Dimensional Topology
• Chapter 7. Cell-like Maps and Q-manifolds
• Chapter 8. Applications
• What Next ?
• BIBLIOGRAPHY
• Index