The most general definition of compactness relies on the notion of open covers and subcovers, which is applicable to topological spaces (and thus to metric spaces and as special cases). In brief, a collection of open sets is said to be an open cover of set if the union of these sets is a superset of . This open cover is said to have a finite subcover if a finite subcollection of the could be found that also covers .
The most general definition of compactness relies on the notion of open covers and subcovers, which is applicable to topological spaces (and thus to metric spaces and as special cases). In brief a collection of open sets is said to be an open cover of set if ,the union of these sets is a superset of . This open cover is said to have a finite subcover if a finite subcollection of the could be found that also covers .