Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings

Abstract

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^q$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.