Definition:Closure (Topology)/Definition 2

Definition
Let $T$ be a topological space.

Let $H \subseteq T$.

The closure of $H$ (in $T\,$) is:
 * $\displaystyle \operatorname{cl} \left({H}\right) := \bigcap \left\{{K \supseteq H: K}\right.$ is closed in $\left.{T}\right\}$

That is, $\operatorname{cl} \left({H}\right)$ is the intersection of all closed sets in $T$ which contain $H$.

The closure of $H$ is denoted on as $\operatorname{cl} \left({H}\right)$ or $H^-$.

Also see

 * Equivalence of Definitions of Topological Closure