nLab T-D-space

A topological space $X$ satisfies the $T_D$ separation axiom if, given any element $a$ of $X$, the singleton subset $\{a\}$ is an open subspace in the induced topology on its own closure. In other words, for every point $a$, there is a neighbourhood $U$ of $a$ such that the intersection of $U$ and $Cl\{a\}$ is $\{a\}$.