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 $d(x,y)+d(y,z)-d(x,z)\ge c$, 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 ${\ell }_{\infty }$.

arXiv commentto appear in Comment.Math.Univ.Carolin

References in corpus (2)

• A lower bound for the equilateral number of normed spaces
• On embeddings of finite subsets of ${\ell }_2$