Definition:Closure (Topology)/Definition 1

Definition
Let $T$ be a topological space.

Let $H \subseteq T$.

The closure of $H$ 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.

Also see

 * Equivalent Definitions for Topological Closure