### Some articles on *finite, finite subcover, subcover*:

Compact Space - Theorems

... A

... A

**finite**union of compact sets is compact ... Any collection of closed subsets of X with the**finite**intersection property has nonempty intersection ... every cover of the space by members of the sub-base has a**finite subcover**(Alexander's sub-base theorem) Every net on X has a convergent subnet (see ...Heine–Borel Theorem - Proof

... Observe first the following if a is a limit point of S, then any

... Observe first the following if a is a limit point of S, then any

**finite**collection C of open sets, such that each open set U ∈ C is disjoint from some neighborhood VU of a, fails to be a cover of S ... Indeed, the intersection of the**finite**family of sets VU is a neighborhood W of a in Rn ... Then C ′ is an open cover of S, but any**finite**subcollection of C ′ has the form of C discussed previously, and thus cannot be an open**subcover**of S ...Heine–Borel Theorem - Generalizations

... be an open cover of E, hence there would be a

... be an open cover of E, hence there would be a

**finite subcover**(Unk) of E, hence the intersection of the Fnk would be empty this implies that Fn is empty for all n larger ... If E were not compact, there would exist a cover (Ul)l of E having no**finite subcover**of E ... sequence of balls (Bn) in E with the radius of Bn is 2−n there is no**finite subcover**(Ul∩Bn)l of Bn Bn+1 ∩ Bn is not empty ...### Famous quotes containing the word finite:

“Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a *finite* vessel from which the more one sister drinks, the less is left for the others.”

—Elizabeth Fishel (20th century)

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