International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 17-26
Research papers

Mackey convergence and quasi-sequentially webbed spaces

Thomas E. Gilsdorf1,2

1Department of Mathematics/Computer Systems, University of Wisconsin-River Falls, River Falls 54022, Wisconsin, USA
2Department of Mathematics, University of North Dakota, Grand Forks 58202, North Dakota, USA

Received 5 April 1990

Copyright © 1991 Thomas E. Gilsdorf. 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.


The problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi-sequentially webbed spaces (see Definition 1). In particular, it is shown that strictly barrelled spaces satisfy the Mackey convergence condition and that they are properly contained in the set of quasi-sequentially webbed spaces. A related problem is that of characterizing those locally convex spaces satisfying the so-called fast convergence condition. A partial solution to this problem is obtained. Several examples are given.