Topological Closure is Closed

Theorem
Let $T$ be a topological space.

Let $H \subseteq T$.

Then the closure $\map \cl H$ of $H$ is closed in $T$.

Proof
From Closure of Topological Closure equals Closure:
 * $\map \cl {\map \cl H} = \map \cl H$

From Set is Closed iff Equals Topological Closure, it follows that $\map \cl H$ is closed.

Also see

 * Topological Closure is Closure Operator