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Infinite-Dimensional Topology: Volume 43 : Prerequisites and Introduction - J. Van Mill

Infinite-Dimensional Topology: Volume 43

Prerequisites and Introduction

Hardcover

Published: 15th December 1988
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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.

...recommended to anyone who wishes to get familiar with infinite-dimensional topology and at the same time learn about some its most beautiful results. Zentralblatt fur Mathematik

Extension Theorems
Topological Spaces
Linear Spaces
Function Spaces
The Michael Selection Theorem and Applications
AR's and ANR's
The Borsuk Homotopy Extension Theorem
Elementary Plane Topology
The Brouwer Fixed-Point Theorem and Applications
The Borsuk-Ulam Theorem
The Poincare Theorem
The Jordan Curve Theorem
Elementary Combinatorial Techniques
Affine Notions
Simplexes
Triangulation
Simplexes in R n
The Brouwer Fixed-Point Theorem
Topologizing a Simplical Complex
Elementary Dimension Theory
The Covering Dimension
Zero-Dimensional Spaces
Translation into Open Covers
The Imbedding Theorem
The Inductive Dimension Functions ind and Ind
Mappings into Spheres
Totally Disconnected Spaces
Various Kinds of Infinite-Dimensionality
Elementary ANR Theory
Some Properties of ANR's
A Characterization of ANR's and AR's
Hyperspaces and the AR-Property
Open Subspaces of ANR's
Characterization of Finite-Dimensional ANR's and AR's
Adjunction Spaces of Compact A(N)R's
An Introduction to Infinite-Dimensional Topology
Constructing New Homeomorphisms from Old. Z-Sets
The Estimated Homeomorphism Extension Theorem for Compacta in s
The Estimated Homeomorphism Extension Theorem
Absorbers
Hilbert Space is Homeomorphic to the Countable Infinite Product of Lines
Inverse Limits
Hilbert Cube Factors
Cell-Like Maps and Q-Manifolds
Cell-Like Maps and Fine Homotopy Equivalences
Z-Sets in ANR's
The Disjoint-Cells Property
Z-Sets in Q-Manifolds
Torunczyk's Approximation Theorem and Applications
Cell-Like Maps
The Characterization Theorem
Applications
Infinite Products
Keller's Theorem
Cone Characterization of the Hilbert Cube
The Curtis-Schori-West Hyperspace Theorem
What Next?
Bibliography
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780444871336
ISBN-10: 0444871330
Series: North-Holland Mathematical Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 416
Published: 15th December 1988
Publisher: Elsevier Science & Technology
Country of Publication: US
Dimensions (cm): 22.23 x 15.88  x 1.91
Weight (kg): 0.72