Metamath Proof Explorer


Theorem pibp16

Description: Property P000016 of pi-base. The class of compact topologies. A space X is compact if every open cover of X has a finite subcover. This theorem is just a relabeled copy of iscmp . (Contributed by ML, 8-Dec-2020)

Ref Expression
Hypothesis pibp16.x X=J
Assertion pibp16 JCompJTopy𝒫JX=yz𝒫yFinX=z

Proof

Step Hyp Ref Expression
1 pibp16.x X=J
2 1 iscmp JCompJTopy𝒫JX=yz𝒫yFinX=z