Some Remarks About Mackey Convergence

Józef Burzyk, Thomas E. Gilsdorf

Research output: Contribution to journalArticlepeer-review

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 Mackey convergence condition and every sequentially continuous seminorm is continuous, then the space is bornological.

Original languageEnglish
Pages (from-to)659-664
Number of pages6
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume18
Issue number4
DOIs
StatePublished - 1995

Keywords

  • Mackey convergence
  • barrelled space
  • bornological space
  • property K

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