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# Volume 64. The Infinite-Dimensional Topology of Function Spaces

## 1st Edition

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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. A `scenic' 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 th

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. A `scenic' 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 th

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.

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.

- No. of pages:
- 642

- Language:
- English

- Copyright:
- © 2001

- Published:
- 15th June 2001

- Imprint:
- North Holland

- Print ISBN:
- 9780444505576

- Electronic ISBN:
- 9780080929491

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

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