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

## TL;DR

This paper proves that certain bounded, countable metric spaces with a specific triangle inequality can be isometrically embedded into any Banach space containing an isomorphic copy of __.

## Contribution

It establishes a new class of metric spaces that can be isometrically embedded into Banach spaces with __, expanding understanding of metric space embeddings.

## Key findings

- Such metric spaces can be embedded into Banach spaces with __.
- The embedding preserves distances exactly.
- The result applies to all Banach spaces containing an isomorphic __.

## 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 $\ell_\infty$.