Weak topology
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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