Overview

This text studies 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. 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. 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 flavour 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: to test the reader's understanding of the material; to supply proofs of statements that are used in the text, but are not proven there; and to provide additional information not covered by the text. Solutions to important or difficult exercises have been included in Appendix B.

Full Product Details

9780444508492

Table of Contents

Reviews

We strongly recommend this book to mathematicians working in C<INF /INF>-theory, infinite-dimensional topology, or dimension theory and also to students interested in these topics. Mathematical Reviews

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.Mathematical Reviews

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available