Isometric embeddings of a class of separable metric spaces into Banach spaces

Abstract

Let (M, d) be a bounded countable metric space and c > 0 a constant, such that d(x, y) + d(y, z) - d(x, z) ≥ c, for any pairwise distinct points x, y, z of M. For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of ℓ∞. © 2018 Charles University, Faculty of Mathematics and Physics