Definition:Closure (Topology)/Definition 4

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

Let $H \subseteq S$.

The closure of $H$ (in $T$) is defined as the union of $H$ and its boundary in $T$:
 * $H^- := H \cup \partial H$

Also see

 * Equivalence of Definitions of Topological Closure