ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Topological space
Open set
Definition D98
Closed set
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
A D11: Set $F \subseteq X$ is closed in $T$ if and only if \begin{equation} X \setminus F \in \mathcal{T} \end{equation}
Children
D2640: Clopen set
Results
R1762: Closed set less open set is closed
R76: Empty set is closed
R2746: Finite sets are closed in Fréchet space
R2747: Finite sets are closed in Hausdorff space
R2748: Finite sets are closed in metric space
R74: Finite union of closed sets is closed
R75: Intersection of closed sets is closed
R4007: Singletons are closed in Polish space
R233: Whole space is closed