TAME TOPOLOGY AND O-MINIMAL STRUCTURES (London Mathematical Society Lecture Note Series 248) By L OU VAN DEN D RIES : 180 pp., £24.95 (US$39.95, LMS Members' price £18.70), ISBN 0 521 59838 9…

By Alex Wilkie. 2000

429 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9f93b813015a37da871838d8f6650945cde10b7c

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Citations in the corpus

On central extensions and definably compact groups in o-minimal structures (2008, background): “7 in [5]) that over the real numbers the definably connected components of definable subsets of Rn are just the usual connected components and then conclude then that kn is constant on every (definably) connected component of the set G(n).”
Definability of restricted theta functions and families of abelian varieties (2011, background): “Since the subject of o-minimality may be not very familiar to some readers we give a brief introduction to the topics and refer to [5, 6] for more detailed expositions.”
Ax–Schanuel for the $j$-function (2014, methodology): “For an introduction to this theory, see [8]; on Ran, exp see [9, 10].”
The Field of Reals with Multisummable Series and the Exponential Function (2000, background): “(See [7, 5] for background and results on o-minimal structures.”
o-minimal GAGA and a conjecture of Griffiths (2018, background): “For a general introduction to o-minimality, see [18], and [19] for a discussion of o-minimality in a similar language to this paper.”
How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms (2018, background): “3 (The Trivialization Theorems of [22]).”
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality (2008, background): “In the last decades powerful advances relying on an axiomatized approach of real-semialgebraic/realanalytic geometry have allowed to set up a general theory in which the basic objects enjoy the same qualitative properties as semialgebraic sets and functions [28, 46, 49].”
Microlocal Morse theory of wrapped Fukaya categories (2018, background): “Wherever we have written ‘subanalytic’, one could substitute ‘defineable’ with respect to any fixed analytic-geometric category [87, 86].”
Fast optimization via inertial dynamics with closed-loop damping (2020, background): “The general notion covering these situations is the concept of o-minimal structure; see van den Dries [82].”
Weakly o-minimal structures and real closed fields (2000, background): “Throughout the paper we assume familiarity with basic results of o-minimality as contained [22] and [14] (see also [9]).”