The Infinite-Dimensional Topology of Function Spaces

ISBN: 9780444505576 出版年：2002 页码：643 Mill, J van North Holland_RM

In this book we study function spaces of low Borel complexity.Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theoryare primarily used for the study of these spaces. The mix ofmethods from several disciplines makes the subjectparticularly 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 ininfinite-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 theDobrowolski-Marciszewski-Mogilski Theorem, linking theresults 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 forgraduate courses in topology. For a course in dimension theory, Chapters 2 and 3 and part of Chapter 1 should be covered.