Geodesic
Isometric embeddings of a class of separable metric spaces into Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 233-239.

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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 $.
DOI : 10.14712/1213-7243.2015.239
Classification : 46B20, 46B26, 46E15, 54D30
Keywords: concave metric space; isometric embedding; separated set 
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Mercourakis, Sophocles K.; Vassiliadis, Vassiliadis G. Isometric embeddings of a class of separable metric spaces into Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 233-239. doi : 10.14712/1213-7243.2015.239. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.239/

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