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.

Preface These notes have served as a basis for a course in Pisa in Spring 1999. A parallel course on the construction of o-minimal structures was given by A. Macintyre. The content of these notes… Expand

On a real analytic manifold M, we construct the linear subanalytic Grothendieck topology Msal together with the natural morphism of sites $\rho$ from Msa to Msal, where Msa is the usual subanalytic… Expand

My goal is to give everyone a sense of the subject of o-minimality, and the literature on this topic has grown vast, so I will ignore a lot of things in order to get at issues relevant for this audience.Expand

Abstract In this paper we present Thom’s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on the… Expand

– We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, ·). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in… Expand