International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 521-524
doi:10.1155/S0161171299225215

Webbed spaces, double sequences, and the Mackey convergence condition

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.