Infinite-Dimensional Topology. Prerequisites and Introduction (North-Holland Mathematical Library Volume 43)

Van Mill, J.

ISBN 10: 0444871330 / ISBN 13: 9780444871336

Published by North Holland, 1988

About this Item

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Bibliographic Details

• Title: Infinite-Dimensional Topology. Prerequisites and Introduction (North-Holland Mathematical Library Volume 43)
• Publisher: North Holland
• Publication Date: 1988
• Language: English
• ISBN 10: 0444871330
• ISBN 13: 9780444871336
• Binding: Hardcover
• Condition: good

About this title

Synopsis

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.

Review

...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 für Mathematik