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
▼ Closure point
Definition D88
Set closure
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $\mathcal{T}_{\text{closed}}$ is the D2439: Set of closed sets in $T$
The closure of $E \subseteq X$ in $T$ is the D11: Set \begin{equation} \text{cl}_T E : = \bigcap \{ F : E \subseteq F \in \mathcal{T}_{\text{closed}} \} \end{equation}
Also known as
Closed hull, Generated closed set
Children
▶ D136: Topologically dense set