Topological Closure

The closure of a subset S ⊆ X 𝑆 𝑋 S\subseteq X of a Topological Space X 𝑋 X , denoted Cl ⁢ ( S ) Cl 𝑆 \mathrm{Cl}(S) or S ¯ ¯ 𝑆 \overline{S} is the intersection

Cl⁢(S)=⋂{X\U∈𝒪⁢(X)}Cl𝑆\𝑋𝑈𝒪𝑋\par\mathrm{Cl}(S)=\bigcap\left\{\;X\backslash U\in\mathcal{O}({X})\right\}

of all Closed Subset of a Topological Space.