Closure

[Definition]{.underline}: Given a set $A \subseteq \mathbb{R}$, let $L$ be the set of all limit_points of $A$. The [[[closure]{.underline}]] of $A$ is defined to be $\overline{A} = A \cup L$.

Theorems

[Theorem]{.underline}: For any $A \subseteq \mathbb{R}$, the closure $\overline{A}$ is a closed_set and is the smallest closed_set containing $A$.