Let $(X,\tau)$ be a [topological space](/page/Topological%20Space), let $A \subset X$, and let $\mathcal U \subset \tau$. Then $\mathcal U$ is an [open cover](/page/Open%20Cover) of $A$ in $X$ if and only if for every $a \in A$ there exists $U \in \mathcal U$ such that $a \in U$.