International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 659-664
doi: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 58202-8376, ND, USA
Received 16 September 1993; Revised 5 March 1994
Copyright © 1995 Józef Burzyk and 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.
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.