## Geometry & Topology

### Definable triangulations with regularity conditions

Małgorzata Czapla

#### 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 $T$ 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.

#### Article information

Source
Geom. Topol., Volume 16, Number 4 (2012), 2067-2095.

Dates
Revised: 18 March 2012
Accepted: 23 April 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732479

Digital Object Identifier
doi:10.2140/gt.2012.16.2067

Mathematical Reviews number (MathSciNet)
MR3033513

Zentralblatt MATH identifier
1375.14188

#### Citation

Czapla, Małgorzata. Definable triangulations with regularity conditions. Geom. Topol. 16 (2012), no. 4, 2067--2095. doi:10.2140/gt.2012.16.2067. https://projecteuclid.org/euclid.gt/1513732479

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