Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 52, Number 3 (2008), 1045-1063.
Lipschitz cell decomposition in o-minimal structures I
A main tool in studying topological properties of sets definable in o-minimal structures is the Cell Decomposition 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.
Illinois J. Math., Volume 52, Number 3 (2008), 1045-1063.
First available in Project Euclid: 1 October 2009
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 32B20: Semi-analytic sets and subanalytic sets [See also 14P15] 14P10: Semialgebraic sets and related spaces
Secondary: 32S60: Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx] 51N20: Euclidean analytic geometry 51F99: None of the above, but in this section
Pawłucki, Wiesław. Lipschitz cell decomposition in o-minimal structures I. Illinois J. Math. 52 (2008), no. 3, 1045--1063. doi:10.1215/ijm/1254403731. https://projecteuclid.org/euclid.ijm/1254403731