(i) | $\mathcal{T}_{\text{closed}}$ is the D2439: Set of closed sets in $T$ |

**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}

▾ 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

▾ 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

Formulation 0

Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that

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}

(i) | $\mathcal{T}_{\text{closed}}$ is the D2439: Set of closed sets in $T$ |

Also known as

Closed hull, Generated closed set

Child definitions