Definition:Open Cover/Subset

Definition
Let $\left({S, \tau}\right)$ be a topological space. Let $H$ be a subset of $S$.

Let $\mathcal C$ be a cover of $H$.

Then $\mathcal C$ is an open cover for $H$ :
 * $\mathcal C \subseteq \tau$

That is, all the elements of $\mathcal C$ are open sets.