Tame Topology and O-minimal Structures (London Mathematical Society Lecture Note Series Book 248) 1st Edition by L. P. D. van den Dries (PDF)

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.

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Purchased this book for a summer readings course at the end of my undergraduate degree. The information is presented very clearly and reads very logically (there is little to no need to jump to other texts to search for obscure material to support the book matter). Not for the faint of heart, however.

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