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  3. Tame Topology and O-minimal Structures
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      May 1998
      ISBN:
      9780511525919
      9780521598385
      DOI:
      https://doi.org/10.1017/CBO9780511525919
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.275kg, 192 Pages
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Real and Complex Analysis
      Series:
      London Mathematical Society Lecture Note Series (248)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Real and Complex Analysis
    Series:
    London Mathematical Society Lecture Note Series (248)
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    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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