On the Lipschitz classification of normed spaces, unit balls, and spheres

Abstract

Abstract. For every normed space Z, we note its closed unit ball and unit sphere by B Z and S Z , respectively. Let X and Y be normed spaces such that S X is Lipschitz homeomorphic to S X⊕R , and S Y is Lipschitz homeomorphic to S Y ⊕R .We prove that the following are equivalent:This result holds also in the uniform category, except (2 or 3) ⇒ 1 which is known to be false.