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Preprint Number 1057

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1057. Małgorzata Czapla and Wiesław Pawłucki
Strict C^1-triangulations in o-minimal structures

Submission date: 13 June 2016


Let R be a real closed field and let an expansion of R to an o-minimal structure be given. We prove that for any closed bounded definable subset A of R^n and a finite family B_1,...,B_r of definable subsets of A there exists a definable triangulation h : |K| −→ A of A compatible with B_1,...,B_r such that K is a simplicial complex in R^n and h extends to a definable C^1 -mapping defined on a definable open neighborhood of |K| in R^n. This improves a recent resut by Ohmoto and Shiota.

Mathematics Subject Classification: Primary 14P10. Secondary 54C60.

Keywords and phrases: o-minimal structure, C^1-triangulation, Whitney condition.

Full text: pdf.

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