subcover

Def pg. 333

The construction of $\mathcal{G}$ is in open cover

If ${\mathcal{G}}^{\prime }$ is a sub-collection of $\mathcal{G}$ such that it’s union also contain origin set $A$, then ${\mathcal{G}}^{\prime }$ is called subcover of $\mathcal{G}$. If ${\mathcal{G}}^{\prime }$ has consist of finitely many set, we can call ${\mathcal{G}}^{\prime }$ a finite subcover of $\mathcal{G}$.

Def 21.4

A subcover of open cover is an open cover