Regular projections and regular covers in o-minimal structures
Tom 130 / 2023
Annales Polonici Mathematici 130 (2023), 63-83
MSC: Primary 32B20; Secondary 14P10.
DOI: 10.4064/ap211206-3-1
Opublikowany online: 28 February 2023
Streszczenie
We prove that for any definable subset $X\subset \mathbb {R}^{n}$ in a polynomially bounded o-minimal structure, with ${\rm dim}(X) \lt n$, there is a finite set of regular projections (in the sense of Mostowski). We also give a weak version of this theorem in any o-minimal structure, and we give a counterexample in o-minimal structures that are not polynomially bounded. As an application we show that in any o-minimal structure there exists a regular cover in the sense of Parusiński.
