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From Encyclopedia of Mathematics
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of a topological vector space

A complete topological vector space such that is a subspace of and is dense in . The transition from to is also called completion; its standard realization is carried out by generalized sequences (in particular, Cauchy sequences, cf. Generalized sequence).


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References

[a1] G. Köthe, "Topological vector spaces" , 1 , Springer (1969)
How to Cite This Entry:
Completion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Completion&oldid=17719
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article