# Definition:Open Cover/Subset

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## Definition

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 $H$ if and only if:

$\CC \subseteq \tau$

That is, if and only if all the elements of $\CC$ are open sets.