Definition:Closure (Topology)/Definition 3

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

Let $H \subseteq S$.

The closure of $H$ (in $T$), denoted $H^-$, is defined as the smallest closed set of $T$ that contains $H$.

Also see

 * Equivalence of Definitions of Topological Closure