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) | $\forall \, E \in \mathcal{C} : X \setminus E \in \mathcal{T}$ |
▼ | Set of symbols |
▼ | Alphabet |
▼ | Deduction system |
▼ | Theory |
▼ | Zermelo-Fraenkel set theory |
▼ | Set |
▼ | Collection of sets |
▼ | Set union |
▼ | Set cover |
▼ | Open set cover |
(1) | $X \subseteq \cup \mathcal{C}$ (D74: Set cover) |
(2) | $\forall \, E \in \mathcal{C} : X \setminus E \in \mathcal{T}$ |