\begin{definition}[Definition:Open Cover/Subset]
Let $\struct {S, \tau}$ be a topological space.
Let $H$ be a subset of $S$.
Let $\CC$ be a cover of $H$.
Then $\CC$ is an '''open cover for $H$''' {{iff}}:
:$\CC \subseteq \tau$
That is, {{iff}} all the elements of $\CC$ are open sets.
\end{definition}