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Lipschitz cell decomposition in o-minimal structures. I. (English) Zbl 1222.32019
Summary: A main tool in studying topological properties of sets definable in o-minimal structures is the cell cecomposition theorem. The present paper proposes its metric counterpart based on the idea of a Lipschitz cell. In contrast to earlier results, we give an algorithm of a Lipschitz cell decomposition involving only permutations of variables as changes of coordinates.

MSC:
32B20 Semi-analytic sets, subanalytic sets, and generalizations
14P10 Semialgebraic sets and related spaces
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
51N20 Euclidean analytic geometry
51F99 Metric geometry
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Full Text: Euclid
References:
[1] L. van den Dries, Tame topology and o-minimal structures , Cambridge Univ. Press, 1998. · Zbl 0953.03045
[2] K. Kurdyka, On a subanalytic stratification satisfying a Whitney property with exponent 1 , Proc. Conference Real Algebraic Geometry—Rennes 1991, Lecture Notes in Math., vol. 1524, Springer, Berlin, 1992, pp. 316–322. · Zbl 0779.32006 · doi:10.1007/BFb0084630
[3] A. Parusiński, Lipschitz stratification of subanalytic sets , Ann. Sci. École Norm. Sup. 27 (1994), 661–696. · Zbl 0819.32007 · numdam:ASENS_1994_4_27_6_661_0 · eudml:82372
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