International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 659-664
doi:10.1155/S0161171295000846
Some remarks about Mackey convergence
Józef Burzyk1
and Thomas E. Gilsdorf2
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
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.