T1 space

Definition

A topological space $X$ is T1 when for all points $x \neq y$ of $X$ there is an open set $U$ with $x \in U$ and $y \notin U$.

Remarks

A space is T1 if and only if each set $\{x\}$ with $x \in X$ is closed. Each Hausdorff space is T1, and each T1 space is T0. An infinite set with the cofinite topology is T1 but not Hausdorff. In fact, the cofinite topology is the coarsest T1 topology on a set.

Explanations

L1 human

In a T1 space, for two distinct points, each point has an open set around it that does not contain the other point. This is the same as saying that single points are closed.