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arXiv · 2110.06391

Regular projections and regular covers in o-minimal structures

M'hammed Oudrane
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Abstract

In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded o-minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak version of this theorem in any o-minimal structure, and we give a counter example in o-minimal structures that are not polynomially bounded. As an application we show that in any o-minimal structure there exist a regular cover in the sense of Parusi\'nski.

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M'hammed Oudrane. 2021-10-12. Regular projections and regular covers in o-minimal structures. https://arxiv.org/abs/2110.06391

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