Solution
= Solution
The <closure> of $A$ is the <intersection> of every <closed> subset containing it:
$$
\boxed{\overline A=\bigcap\{F\subseteq X:F\text{ closed and }A\subseteq F\}.}
$$
The collection is nonempty because it contains $X$. Arbitrary <intersections> of <closed> sets are <closed>, so this is the smallest <closed> set containing $A$.