The geometry of Hamming-type metrics and their embeddings into Banach spaces

Within the class of reflexive Banach spaces, we prove a metric characterization asymptotic-c0 spaces in terms bi-Lipschitz invariant which involves metrics that generalize Hamming on k-subsets ℕ. We apply this to show separable, reflexive, and is non-Borel co-analytic. Finally, introduce relaxation property, called asymptotic-subsequential-c0 partial obstruction equi-coarse embeddability sequence graphs. present examples are asymptotic-subsequential-c0. In particular, T*(T*) where T* Tsirelson’s original space.