Regular projections and regular covers in ominimal structures
Abstract
In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded ominimal 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 ominimal structure, and we give a counter example in ominimal structures that are not polynomially bounded. As an application we show that in any ominimal structure there exist a regular cover in the sense of Parusiński.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06391
 Bibcode:
 2021arXiv211006391O
 Keywords:

 Mathematics  Metric Geometry