Namespaces
Variants
Actions

Weak topology

From Encyclopedia of Mathematics
Revision as of 17:20, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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=28283
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article