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Tame Topology and O-minimal Structures : London Mathematical Society Lecture Note Series - Lou van den Dries

Tame Topology and O-minimal Structures

London Mathematical Society Lecture Note Series

Paperback Published: 6th July 1998
ISBN: 9780521598385
Number Of Pages: 192

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Following their introduction in the early 1980s, o-minimal structures have provided an elegant and surprisingly efficient generalization of semialgebraic and subanalytic geometry. This book gives a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. It 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.

"...indispensable to any student or research interested in o-minimal structures. ...written with remarkable precision and clarity..." Bulletin of the AMS "This is an excellent textbook..." Bulletin of Symbolic Logic

Some elementary results
Semialgebraic sets
Cell decomposition
Definable invariants: Dimension and Euler characteristic
The Vapnik-Chernovenkis property in o-minimal structures
Point-set topology in o-minimal structures
Smoothness
Triangulation
Trivialization
Definable spaces and quotients
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521598385
ISBN-10: 0521598389
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 192
Published: 6th July 1998
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.88  x 0.64
Weight (kg): 0.27