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Regular projections and regular covers in o-minimal structures

Volume 130 / 2023

M’hammed Oudrane Annales Polonici Mathematici 130 (2023), 63-83 MSC: Primary 32B20; Secondary 14P10. DOI: 10.4064/ap211206-3-1 Published online: 28 February 2023

Abstract

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.

Authors

  • M’hammed OudraneUniversité Côte d’Azur
    CNRS, Labo. J.-A. Dieudonné, UMR CNRS 7351
    06108 Nice, France
    e-mail

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