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}