Tame Topology and O-minimal Structures (London Mathematical Society Lecture Note Series)

Dries, L. P. D. van den

Cambridge University Press（1998/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 192 p.
• 言語 ENG
• 商品コード 9780521598385
• DDC分類 514

Full 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.

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.