(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}

Definition D88

Set closure

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 $T$ |

Children

▶ | Topologically dense set |