Definition:Open Cover

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

Let $H$ be a subset of $S$.

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

Then $\mathcal C$ is an open cover for $H$ iff $\mathcal C \subseteq \tau$.

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

In particular, $H$ may equal $S$ in this definition.