Tame topology and o-minimal structures
Author(s)
Bibliographic Information
Tame topology and o-minimal structures
（London Mathematical Society lecture note series, 248）
Cambridge University Press, 1998
- : pbk
Available at / 67 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||LMS||24898022239
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
pbk.DC21:514/V2822070438237
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
Following their introduction in the early 1980s o-minimal structures were found to provide an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. The book starts with an introduction and overview of the subject. Later chapters cover the monotonicity theorem, cell decomposition, and the Euler characteristic in the o-minimal setting and show how these notions are easier to handle than in ordinary topology. The remarkable combinatorial property of o-minimal structures, the Vapnik-Chervonenkis property, is also covered. This book should be of interest to model theorists, analytic geometers and topologists.
Table of Contents
- 1. Some elementary results
- 2. Semialgebraic sets
- 3. Cell decomposition
- 4. Definable invariants: Dimension and Euler characteristic
- 5. The Vapnik-Chernovenkis property in o-minimal structures
- 6. Point-set topology in o-minimal structures
- 7. Smoothness
- 8. Triangulation
- 9. Trivialization
- 10. Definable spaces and quotients.
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