Noun
subcover (plural subcovers)
(topology) A cover which is a subset of another cover.
The open intervals cover the real numbers; the open intervals of the form (x, x+1) are a subcover.
;Countably compact: A space is countably compact if every countable open cover has a finite subcover. Source: Internet
Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover. Source: Internet
; Compact : A space is compact if every open cover has a finite subcover. Source: Internet
Peter Gustav Lejeune Dirichlet was the first to prove this and implicitly he used the existence of a finite subcover of a given open cover of a closed interval in his proof. Source: Internet
;Subcover: A cover K is a subcover (or subcovering) of a cover L if every member of K is a member of L. ;Subcovering: See Subcover. Source: Internet
The collection of all singletons of the space is an open cover which admits no finite subcover. Source: Internet