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International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 473-483
http://dx.doi.org/10.1155/S0161171288000559

The Mackey convergence condition for spaces with webs

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, WA, USA

Received 3 December 1987

Copyright © 1988 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

If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.