Hausdorff

Hausdorff Space

A topological space $X$ is Hausdorff iff for every pair of distinct points $x,y\in X$, there exist open sets $U,V\subseteq X$ such that:

• $x\in U$,
• $y\in V$,
• $U\cap V=\varnothing$.

Equivalently, any two distinct points can be separated by disjoint open neighbourhoods.