# Completion

From Encyclopedia of Mathematics

*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).

#### Comments

#### 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