#### Volume 16, issue 4 (2012)

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Definable triangulations with regularity conditions

### Małgorzata Czapla

Geometry & Topology 16 (2012) 2067–2095
##### Abstract

We prove that every definable in an o-minimal structure 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 $\mathsc{T}$ of regularity conditions and give a universal construction of a definable triangulation with a $\mathsc{T}$ condition of a definable set. This class includes the Whitney (B) and the Verdier conditions.

##### Keywords
Weakly Lipschitz mapping, definable triangulation, Whitney (B) condition, Verdier condition
##### Mathematical Subject Classification 2010
Primary: 14P05, 14P10, 32B20, 32B25