ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Collection of sets
Set union
Set cover
Open set cover
Definition D4448
Closed set cover
Formulation 0
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) $\forall \, E \in \mathcal{C} : X \setminus E \in \mathcal{T}$