Metrically Convex Space

Metrically Convex SpaceA metric space $(M,d)$ is said to be metrically convex if for anytwo points $x,y\in M$ with $x\ne y$ there exists $z\in M$: $x\ne z\ne y$, such that$d(x,z)+d(z,y)=d(x,y)$.