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International Journal of Mathematics and Mathematical Sciences
Volume 22, Issue 3, Pages 521-524
http://dx.doi.org/10.1155/S0161171299225215

Webbed spaces, double sequences, and the Macke convergence condition

Instituto de Matemáticas, U.N.A.M., Area de la Investigación Científica, Circuito Exterior, Ciudad Universitaria, México D.F. 04510, Mexico

Received 28 April 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In [3], Gilsdorf proved, for locally convex spaces, that every sequentially webbed space satisfies the Mackey convergence condition. In the more general frame of topological vector spaces, this theorem and its inverse are studied. The techniques used are double sequences and the localization theorem for webbed spaces.