▾ 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
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
Child definitions
» D136: Topologically dense set