= Solution
The <closure> $\overline A$ is the <intersection> of every <closed subset> of $X$ containing $A$. Thus it is the smallest such <closed subset>. Equivalently,
$$
\boxed{x\in\overline A\iff\text{every open neighbourhood of }x\text{ meets }A.}
$$
For equivalence, if an <open neighbourhood> misses $A$, its <complement> is a <closed> superset of $A$ missing $x$. Conversely, a <closed> superset missing $x$ has an <open> <complement> that is a neighbourhood of $x$ disjoint from $A$.
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