Regular projections and regular covers in o-minimal structures
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 Parusiński.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2021
- arXiv:
- arXiv:2110.06391
- Bibcode:
- 2021arXiv211006391O
- Keywords:
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- Mathematics - Metric Geometry