# Weak topology

From Encyclopedia of Mathematics

The locally convex topology on a vector space generated by the family of semi-norms (cf. Semi-norm) , where ranges over some subset of the (algebraic) adjoint space .

#### References

[1] | L.A. Lyusternik, V.I. Sobolev, "A short course of functional analysis" , Moscow (1982) (In Russian) |

[2] | H.H. Schaefer, "Topological vector spaces" , Springer (1971) |

#### Comments

The weak topology as introduced above is often denoted by . It is a Hausdorff topology if and only if separates the points of .

See also Strong topology.

#### References

[a1] | H. Jarchow, "Locally convex spaces" , Teubner (1981) (Translated from German) |

**How to Cite This Entry:**

Weak topology.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Weak_topology&oldid=17244

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article