Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2009, September 2.

Abstract:
We prove that every definable set has a definable triangulation which is locally Lipschitz and weakly bi-Lipschitz on the natural simplicial stratification of a simplicial complex. We also distinguish a class T of regularity conditions and give a universal construction of a definable triangulation with a T condition of a definable set. This class includes the Whitney (B) and the Verdier conditions.

Mathematics Subject Classification (2000): 14P05, 14P10, 32B20, 32B25.

Keywords and Phrases: weakly Lipschitz mapping, definable triangulation, Whitney (B) condition, Verdier conditions.

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