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Preprint Number 1057
1057. Małgorzata Czapla and Wiesław Pawłucki Strict C^1triangulations in ominimal structures Email: Submission date: 13 June 2016 Abstract: Let R be a real closed field and let an expansion of R to an ominimal 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: ominimal structure, C^1triangulation, Whitney condition. Full text: pdf.

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