Def pg. 333

The construction of 𝒢︀ is in open cover

If 𝒢︀ is a sub-collection of 𝒢︀ such that it’s union also contain origin set 𝐴, then 𝒢︀ is called subcover of 𝒢︀. If 𝒢︀ has consist of finitely many set, we can call 𝒢︀ a finite subcover of 𝒢︀.

Def 21.4

A subcover of open cover is an open cover