Metric Space with Interpolation Points

In the setting of The Real Numbers: Standing Notation and Background, let $(X,d)$ be a metric space.

¶The metric space $(X,d)$ has interpolation points if for all $x,y\in X$ and every $t\in\mathbb{R}$ with $0\le t\le1$ there is $z\in X$ such that

such a point $z$ is called an interpolation point of $x$ and $y$ at parameter $t$.