Regular projections in o-minimal structures

Abstract

In this paper, we prove that for a given definable set X⊂Rn with empty interior there exists a definable bi-Lipschitz homeomorphism h:Rn→Rn such that h(X) has a finite set of regular projections (in the sense of Mostowski). A consequence of this result is the existence of definable regular covers for definable sets, which is a positive answer to a question of Parusiński.