Closure

Definition

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

Theorems

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