Countably compact space
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness
Definition
Symbol-free definition=
A topological space is said to be countably compact if every countable open cover has a finite subcover. In other words, given a countable collection of open subsets whose union is the whole space, there is a finite subcollection whose union is again the whole space.
Formalisms
Refinement formal expression
In the refinement formalism, a refinement formal expression is:
Countable open Finite open
viz, every countable open cover has a finite open refinement.
It is also an instance of the countably qualifier applied to compactness-like properties.