The Lipschitz type of the Geometric Directional Bundle

In this paper we investigate the behaviour of the geometric directional bundles, associated to arbitrary subsets in R^n, under bi-Lipschitz homeomorphisms, and give conditions under which their bi-Lipschitz type is preserved. The most general sets we consider satisfy the sequence selection property (SSP) and, consequently, we investigate the behaviour of such sets under bi-Lipschitz homeomorphisms as well. In particular, we show that the bi-Lipschitz images of a subanalytic sets generically satisfy the (SSP) property.