# Metrically Convex Space

Metrically Convex Space A metric space $(M,d)$ is said to be metrically convex if for any two points $x,y\in M$ with $x\not=y$ there exists $z\in M$: $x\not=z\not=y$, such that $d(x,z)+d(z,y)=d(x,y)$.