Geometry & Topology
- Geom. Topol.
- Volume 16, Number 4 (2012), 2067-2095.
Definable triangulations with regularity conditions
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 of regularity conditions and give a universal construction of a definable triangulation with a condition of a definable set. This class includes the Whitney (B) and the Verdier conditions.
Geom. Topol., Volume 16, Number 4 (2012), 2067-2095.
Received: 26 February 2011
Revised: 18 March 2012
Accepted: 23 April 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14P05: Real algebraic sets [See also 12D15, 13J30] 14P10: Semialgebraic sets and related spaces 32B20: Semi-analytic sets and subanalytic sets [See also 14P15] 32B25: Triangulation and related questions
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