Tame Topology and O-Minimal Structures

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Sprache: Englisch

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Beschreibung

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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2003
Fachbereich:	Geometrie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9780521598385
ISBN-10:	0521598389
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Dries, Lou van den Dries, L. P. D. Van Den
Redaktion:	Cassels, J. W. S.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 11 mm
Von/Mit:	Lou van den Dries (u. a.)
Erscheinungsdatum:	27.11.2003
Gewicht:	0,287 kg