Definition:Closure (Topology)/Definition 1

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$.

The closure of $H$ (in $T$) is defined as:
 * $H^- := H \cup H'$

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

That is, $H^-$ is the union of $H$ and its limit points.

Also see

 * Equivalence of Definitions of Topological Closure