Urysohn space

Summary

An Urysohn space is a topological space in which any two distinct points have disjoint closed neighbourhoods. This separation axiom, also written $T_{2\frac12}$, lies between Hausdorff and regular Hausdorff. Every Urysohn space is Hausdorff, and every regular Hausdorff space is Urysohn. Some authors use the name for the stronger notion of a completely Hausdorff space.