Definition:Subcover

Let $$S$$ be a set.

Let $$\mathcal{U}$$ be a cover for $$S$$.

A subcover of $$\mathcal{U}$$ for $$S$$ is a set $$\mathcal{V} \subseteq \mathcal{U}$$ such that $$\mathcal{V}$$ is also a cover for $$S$$.