Closure is closed

Statement

Let $X$ be a topological space and let $S \subseteq X$. Then the closure $\overline{S}$ is a closed set of $X$.

Remarks

Proof: $\overline{S}$ is an intersection of closed sets, and each intersection of closed sets is closed. It follows that $\overline{\overline{S}} = \overline{S}$.

Explanations

L1 human

The closure is built as an intersection of closed sets, and such an intersection is again closed.