Math and science::Topology
Compactness. Examples
- The collection of sets
form an open cover of . This cover has [no finite subcover/a finite subcover?]. - Divide the interval
like so: , for , then form the cover . This is an open cover, and has many finite subcovers (e.g. ([0, 1/2), (1/2, 1], (1/4, 1]). So we can say that is [...]. - The compact subspaces of
are the [...]. - Any indiscrete space is [compact/not compact, possibly with conditions].
- Any finite space is [compact/not compact, possibly with conditions].
- A discrete space is [compact/not compact, possibly with conditions].
- In a normed vector space
, the closed unit ball is [compact/not compact, possibly with conditions].