In a general topological space, compactness is defined using open covers: a topological space X is compact if and only if every open cover of X has a finite subcover. This means any collection of open sets that covers X can be reduced to a finite number of open sets that still cover X.
Conditions: X is a topological space.; An open cover is a collection of open sets whose union contains X.; A subcover is a subcollection of the open cover that still covers X.
In a general topological space, compactness is defined using open covers: a topological space X is compact if and only if every open cover of X has a finite subcover. This means any collection of open sets that covers X can be reduced to a finite number of open sets that still cover X.
Conditions: X is a topological space.; An open cover is a collection of open sets whose union contains X.; A subcover is a subcollection of the open cover that still covers X.