  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.
