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  3. Tame Topology and O-minimal Structures
  • Cited by 493
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
1998
Online ISBN:
9780511525919
DOI:
https://doi.org/10.1017/CBO9780511525919
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Real and Complex Analysis
Series:
London Mathematical Society Lecture Note Series (248)
Information

Book 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.

Reviews

"...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

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