Illinois Journal of Mathematics

Lipschitz cell decomposition in o-minimal structures I

Wiesław Pawłucki

Full-text: Open access


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.

Article information

Illinois J. Math., Volume 52, Number 3 (2008), 1045-1063.

First available in Project Euclid: 1 October 2009

Permanent link to this document

Digital Object Identifier

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.

Export citation


  • L. van den Dries, Tame topology and o-minimal structures, Cambridge Univ. Press, 1998.
  • 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.
  • A. Parusiński, Lipschitz stratification of subanalytic sets, Ann. Sci. École Norm. Sup. 27 (1994), 661–696.