A D11: Set $F \subseteq X$ is

**closed**in $T$ if and only if \begin{equation} X \setminus F \in \mathcal{T} \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

▾ Open set

▾ 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

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}

A D11: Set $F \subseteq X$ is

Dual definition

» Open set

Child definitions

Results