Webbed spaces, double sequences, and the Macke 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.

Keywords

• Compatible double sequence
• compatible web
• Mackey convergent sequence
• sequential double sequence.