Hausdorff

Definition

If there are two points $x$ and $y$ in a topological space $X$ that can be separated by neighbourhoods if there exists a neighbourhood $U$ of $x$ and a neighbourhood $V$ of $y$, such that $U$ and $V$ are disjoint $U\cup V=\varnothing$.

$X$ is a Hausdorff space if any two distinct points in $X$ are separated by neighbourhoods.