Let $(X, \mathcal{T})$ be a [[Topological Spaces|topological space]]. > [!NOTE] Definition > We say that $(X, \mathcal{T})$ is *Hausdorff* iff for all distinct $x,y \in X$, there exists open sets $U, V \in \mathcal{T}$ such that $x\in U$, $y \in V$ and $U \cap V = \emptyset$. # Properties We have that [[Sequences in Hausdorff Spaces Have at Most One Limit|sequences in Hausdorff spaces have at most one limit]]. In relation with compactness, [[Compact Subspaces of Hausdorff Spaces are Closed]].