Set is Subset of its Topological Closure

Theorem
Let $T$ be a topological space.

Let $H \subseteq T$.

Let $H^-$ be the closure of $H$ in $T$.

Then:
 * $H \subseteq H^-$

Proof
From the definition of closure, we have:
 * $H^-$ is the union of $H$ and its limit points.

From Subset of Union it follows directly that:


 * $H \subseteq H^-$