complete metric space

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complete metric space [kəm′plēt ¦me·trik ′spās]

(mathematics)

A metric space in which every Cauchy sequence converges to a point of the space. Also known as complete space.

(theory)

complete metric space - A metric space in which every sequence that converges in itself has a limit. For example, the space of real numbers is complete by Dedekind's axiom, whereas the space of rational numbers is not - e.g. the sequence a[0]=1; a[n_+1]:=a[n]/2+1/a[n].

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analytic set
Baire's category theorem

complete
complete space

completion
Polish space

Souslin's theorem
topologically complete space

uniform boundedness principle

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