A D11: Set $\mathcal{S} \subseteq \mathcal{P}(X)$ is a closed partition of $X$ with respect to $T$ if and only if
| (1) | $\forall \, E, F \in \mathcal{S} \, (E \neq F \quad \Rightarrow \quad E \cap F = \emptyset)$ |
| (2) | $X = \cup \mathcal{S}$ |
| (3) | $\forall \, E \in \mathcal{S} : E \neq \emptyset$ |
| (4) | $\forall \, E \in \mathcal{S} : X \setminus E \in \mathcal{T}$ |