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

Sophocles K. Mercourakis; Vassiliadis G. Vassiliadis — 2018

Commentationes Mathematicae Universitatis Carolinae

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 $ℓ_{\infty}$ .

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