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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.

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
Full Text: Euclid
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