The Infinite-Dimensional Topology of Function Spaces
| Author/creator | Mill, J. van Author |
| Format | Electronic |
| Publication Info | North Holland [Imprint] San Diego : Elsevier Science & Technology Books |
| Description | 644 p. ill 22.000 x 016.000 cm. |
| Supplemental Content | Full text available from eBook - Mathematics pre-2007 |
| Subjects |
| Series | North-Holland Mathematical Studies Vol. 64 |
| Summary | Annotation In this book we study function spaces of low Borel complexity.<br />Techniques from general topology, infinite-dimensional topology, functional analysis and descriptive set theory<br />are primarily used for the study of these spaces. The mix of<br />methods from several disciplines makes the subject<br />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.<br /><br />In order to understand what is going on, a solid background in<br />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<br />Dobrowolski-Marciszewski-Mogilski Theorem, linking the<br />results needed for its proof to interesting recent research developments in dimension theory and infinite-dimensional topology.<br /><br />The first five chapters of this book are intended as a text for<br />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<br />more suitable as a text for a research seminar. The book<br />consequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless stated<br />otherwise, all spaces under discussion are separable and<br />metrizable. In Chapter 6 results for more general classes of spaces are presented.<br /><br />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.<br /><br />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<br />3) to provide additional information not covered by the text.<br />Solutions to selected exercises have been included in Appendix B.<br />These exercises are important or difficult.<br /> |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2001033438 |
| ISBN | 9780444505576 |
| ISBN | 0444505571 (Trade Cloth) Active Record |
| Standard identifier# | 9780444505576 |
| Stock number | 00991439 |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |