Definition:Closure (Topology)/Definition 1

Definition
Let $T$ be a topological space.

Let $H \subseteq T$.

The closure of $H$ (in $T\,$) is:
 * $\operatorname{cl} \left({H}\right) := H \cup H'$

where $H'$ is the derived set of $H$.

That is, $\operatorname{cl} \left({H}\right)$ is the union of $H$ and its limit points.

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

Also see

 * Equivalence of Definitions of Topological Closure