Definition:Open Cover

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

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

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

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

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