Sophocles K. Mercourakis, Vassiliadis G. Vassiliadis
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 $d(x,y)+d(y,z)-d(x,z)\geq c$, 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 $.

Keywords: concave metric space; isometric embedding; separated set

DOI: DOI 10.14712/1213-7243.2015.239
AMS Subject Classification: 46B20 46E15 46B26 54D30