Interpolating metric space
= Interpolating metric space
A metric space $X$ is interpolating when $d(x,y)=r+s$ implies that some $z$ satisfies $d(x,z)=r$ and $d(z,y)=s$. Interpolation makes the <metric exponential candidate> satisfy the triangle inequality, so every bounded interpolating metric space is an <exponentiable object> of $\mathbf{Met}_b$.