Tame Topology and O-minimal Structures
Seiten
1998
Cambridge University Press (Verlag)
978-0-521-59838-5 (ISBN)
Cambridge University Press (Verlag)
978-0-521-59838-5 (ISBN)
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. This book should be of interest to model theorists, analytic geometers and topologists.
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.
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.
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.
| Erscheint lt. Verlag | 7.5.1998 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 275 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-521-59838-9 / 0521598389 |
| ISBN-13 | 978-0-521-59838-5 / 9780521598385 |
| Zustand | Neuware |
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