The Infinite-Dimensional Topology of Function Spaces - 1st Edition - ISBN: 9780444505576, 9780080929774

The Infinite-Dimensional Topology of Function Spaces, Volume 64

1st Edition

Authors: J. van Mill
eBook ISBN: 9780080929774
Hardcover ISBN: 9780444505576
Imprint: North Holland
Published Date: 15th June 2001
Page Count: 642
Tax/VAT will be calculated at check-out Price includes VAT (GST)
30% off
30% off
30% off
30% off
30% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
25% off
25% off
25% off
25% off
25% off
20% off
20% off
30% off
30% off
30% off
30% off
30% off
20% off
20% off
106.00
74.20
74.20
74.20
74.20
74.20
84.80
84.80
63.99
44.79
44.79
44.79
44.79
44.79
51.19
51.19
9300.00
6975.00
6975.00
6975.00
6975.00
6975.00
7440.00
7440.00
79.95
55.97
55.97
55.97
55.97
55.97
63.96
63.96
Unavailable
Price includes VAT (GST)
× DRM-Free

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Table of Contents

Introduction.
Chapter 1. Basic topology. Chapter 2. Basic combinatorial topology. Chapter 3. Basic dimension theory. Chapter 4. Basic ANR theory. Chapter 5. Basic infinite-dimensional topology. Chapter 6. Function spaces. Appendix A. Preliminaries. Appendix B. Answers to selected exercises. Appendix C. Notes and comments. Bibliography. Special Symbols. Author Index. Subject Index.


Description

In this book we study function spaces of low Borel complexity. Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theory are primarily used for the study of these spaces. The mix of methods from several disciplines makes the subject particularly interesting. Among other things, a complete and self-contained proof of the Dobrowolski-Marciszewski-Mogilski Theorem that all function spaces of low Borel complexity are topologically homeomorphic, is presented.

In order to understand what is going on, a solid background in infinite-dimensional topology is needed. And for that a fair amount of knowledge of dimension theory as well as ANR theory is needed. The necessary material was partially covered in our previous book Infinite-dimensional topology, prerequisites and introduction'. A selection of what was done there can be found here as well, but completely revised and at many places expanded with recent results. Ascenic' route has been chosen towards the Dobrowolski-Marciszewski-Mogilski Theorem, linking the results needed for its proof to interesting recent research developments in dimension theory and infinite-dimensional topology.

The first five chapters of this book are intended as a text for graduate courses in topology. For a course in dimension theory, Chapters 2 and 3 and part of Chapter 1 should be covered. For a course in infinite-dimensional topology, Chapters 1, 4 and 5. In Chapter 6, which deals with function spaces, recent research results are discussed. It could also be used for a graduate course in topology but its flavor is more that of a research monograph than of a textbook; it is therefore more suitable as a text for a research seminar. The book consequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless stated otherwise, all spaces under discussion are separable and metrizable. In Chapter 6 results for more general classes of spaces are presented.

In Appendix A for easy reference and some basic facts that are important in the book have been collected. The book is not intended as a basis for a course in topology; its purpose is to collect knowledge about general topology.

The exercises in the book serve three purposes: 1) to test the reader's understanding of the material 2) to supply proofs of statements that are used in the text, but are not proven there 3) to provide additional information not covered by the text. Solutions to selected exercises have been included in Appendix B. These exercises are important or difficult.


Details

No. of pages:
642
Language:
English
Copyright:
© North Holland 2001
Published:
Imprint:
North Holland
eBook ISBN:
9780080929774
Hardcover ISBN:
9780444505576

Reviews

@qu:We strongly recommend this book to mathematicians working in Cp-theory, infinite-dimensional topology, or dimension theory and also to students interested in these topics. @source:Mathematical Reviews


About the Authors

J. van Mill Author

Affiliations and Expertise

Vrije Universiteit, Department of Mathematics and Computer Science, Amsterdam, The Netherlands