A D1106: Topological space $T = (X, \mathcal{T})$ is a Hausdorff topological space if and only if \begin{equation} \forall \, x, y \in X \left( x \neq y \quad \implies \quad \exists \, U, V \in \mathcal{T} : U \cap V = \emptyset, x \in U, y \in V \right) \end{equation}