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 language | English |
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Pages (from-to) | 659-664 |
Number of pages | 6 |
Journal | International Journal of Mathematics and Mathematical Sciences |
Volume | 18 |
Issue number | 4 |
DOIs | |
State | Published - 1995 |
Keywords
- Mackey convergence
- barrelled space
- bornological space
- property K