Definition:Closure (Topology)/Definition 4

Definition
Let $T$ be a topological space.

Let $H \subseteq T$.

The closure of $H$ (in $T$) is the union of $H$ and its boundary in $T$.

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

Also see

 * Equivalence of Definitions of Topological Closure