We investigate the behaviour of the geometric directional bundles, associated to arbitrary subsets in \(\mathbb {R}^n\) , 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 subanalytic sets generically satisfy (SSP).
