Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
A D11: Set $\mathcal{C} \subseteq \mathcal{P}(X)$ is a closed cover for $X$ with respect to $T$ if and only if

(1)	$X \subseteq \cup \mathcal{C}$ (D74: Set cover)
(2)	$\forall \, E \in \mathcal{C} : X \setminus E \in \mathcal{T}$