Convex metric space

This article defines a property that can be evaluated for a metric space

Definition

A metric space $(X,d)$ is said to be convex if given any two distinct points $x,y\in X$, there exists a third distinct point $z\in X$ such that $z$ is between $x$ and $y$, in the following sense:

$d(x,z)+d(z,y)=d(x,y)$