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International Journal of Mathematics and Mathematical Sciences
Volume 18, Issue 4, Pages 659-664
http://dx.doi.org/10.1155/S0161171295000846

Some remarks about Mackey convergence

1Institute of Mathematics, Polish Academy of Science, Wieczorka 8, Katowice 40-013, Poland
2Department of Mathematics, University of North Dakota, Grand Forks, ND 58202-8376, USA

Received 16 September 1993; Revised 5 March 1994

Copyright © 1995 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 this paper, we examine Mackey convergence with respect to K-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K- convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence condition, is barrelled, but is not bornological; and if a space satisfies the biackey convergence condition and every sequentially continuous seminorm is continuous, then the space is bornological.