Definition:Closure (Topology)/Definition 2

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

Let $H \subseteq S$.

The closure of $H$ (in $T$) is defined as:
 * $\displaystyle H^- := \bigcap \left\{{K \supseteq H: K}\right.$ is closed in $\left.{T}\right\}$

That is, $H^-$ is the intersection of all closed sets in $T$ which contain $H$.

Also see

 * Equivalence of Definitions of Topological Closure