The Infinite-Dimensional Topology of Function Spaces

In this book we study function spaces of low Borel complexity.Techniques from general topology infinitedimensional topology functionalanalysis and descriptive s... » 

In this book we study function spaces of low Borel complexity.Techniques from general topology infinitedimensional topology functionalanalysis 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 selfcontainedproof of the DobrowolskiMarciszewskiMogilski Theorem that all function spacesof low Borel complexity are topologically homeomorphic is presented.In order to understand what is going on a solid background ininfinitedimensional topology is needed. And for that a fair amount ofknowledge of dimension theory as well as ANR theory is needed. The necessarymaterial was partially covered in our previous book Infinitedimensionaltopology prerequisites and introduction. A selection of what was done therecan be found here as well but completely revised and at many places expandedwith recent results. A scenic route has been chosen towards theDobrowolskiMarciszewskiMogilski Theorem linking theresults needed for its proof to interesting recent research developments indimension theory and infinitedimensional 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 and3 and part of Chapter 1 should be covered. For a course in infinitedimensionaltopology Chapters 1 4 and 5. In Chapter 6 which deals with function spacesrecent research results are discussed. It could also be used for a graduatecourse in topology but its flavor is more that of a research monograph than ofa textbook it isthereforemore suitable as a text for a research seminar. The bookconsequently has the character of both textbook and a research monograph. InChapters 1 through 5 unless statedotherwise all spaces under discussion are separable andmetrizable. In Chapter 6 results f «