Difference between revisions of "Totally bounded"
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==Definition== | ==Definition== | ||
A [[metric space]] {{M|(X,d)}} is ''totally bounded'' if{{rITTGG}}: | A [[metric space]] {{M|(X,d)}} is ''totally bounded'' if{{rITTGG}}: | ||
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Demote once content added - MOVE TO OWN PAGE, as there are probably other kinds of totally bounded
Definition
A metric space (X,d) is totally bounded if[1]:
- ∀ϵ>0∃n∈N∃{Bi}ni=1 of open balls of radius ϵ[X⊆∪ni=1Bi], that is:
- ∀ϵ>0 there exists a finite collection of open balls, each of radius ϵ, such that the family of balls cover X
