Completely regular or Uniformizable

A space in which points and closed sets can be separated by a function.

Namely, given a closed set $A$ and a point $b \notin A$, there is a continuous function $f:X \rightarrow [0,1]$ such that $f(A) = \{0\}$ and $f(b)=1$.

Defined in 14.8 of MR MR2048350.

Equivalently, the topology is induced by a uniformity. See Theorem 38.2 in MR MR2048350 and Wikipedia Uniform_space.