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The Infinite-Dimensional Topology of Function Spaces, Volume 64 (Hardcover, 1st ed)
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The Infinite-Dimensional Topology of Function Spaces, Volume 64 (Hardcover, 1st ed)
Series: North-Holland Mathematical Library
Expected to ship within 10 - 15 working days
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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 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.
General
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