Mackey convergence and quasi-sequentially webbed spaces
The problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi-sequentially webbed spaces (see Definition 1). In part...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000029 |
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| _version_ | 1832563936768032768 |
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| author | Thomas E. Gilsdorf |
| author_facet | Thomas E. Gilsdorf |
| author_sort | Thomas E. Gilsdorf |
| collection | DOAJ |
| description | The problem of characterizing those locally convex spaces satisfying the Mackey
convergence condition is still open. Recently in [4], a partial description was given using
compatible webs. In this paper, those results are extended by using quasi-sequentially webbed
spaces (see Definition 1). In particular, it is shown that strictly barrelled spaces satisfy the Mackey
convergence condition and that they are properly contained in the set of quasi-sequentially webbed
spaces. A related problem is that of characterizing those locally convex spaces satisfying the so-called
fast convergence condition. A partial solution to this problem is obtained. Several
examples are given. |
| format | Article |
| id | doaj-art-b35f8d9b369745f5980117f9d8a52d19 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b35f8d9b369745f5980117f9d8a52d192025-02-03T01:12:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-01141172610.1155/S0161171291000029Mackey convergence and quasi-sequentially webbed spacesThomas E. Gilsdorf0Department of Mathematics/Computer Systems, University of Wisconsin-River Falls, River Falls, Wisconsin 54022, USAThe problem of characterizing those locally convex spaces satisfying the Mackey convergence condition is still open. Recently in [4], a partial description was given using compatible webs. In this paper, those results are extended by using quasi-sequentially webbed spaces (see Definition 1). In particular, it is shown that strictly barrelled spaces satisfy the Mackey convergence condition and that they are properly contained in the set of quasi-sequentially webbed spaces. A related problem is that of characterizing those locally convex spaces satisfying the so-called fast convergence condition. A partial solution to this problem is obtained. Several examples are given.http://dx.doi.org/10.1155/S0161171291000029webbed spacequasi-sequentially webbed spaceMackey convergencefast convergencelocal completenessinductive limit. |
| spellingShingle | Thomas E. Gilsdorf Mackey convergence and quasi-sequentially webbed spaces International Journal of Mathematics and Mathematical Sciences webbed space quasi-sequentially webbed space Mackey convergence fast convergence local completeness inductive limit. |
| title | Mackey convergence and quasi-sequentially webbed spaces |
| title_full | Mackey convergence and quasi-sequentially webbed spaces |
| title_fullStr | Mackey convergence and quasi-sequentially webbed spaces |
| title_full_unstemmed | Mackey convergence and quasi-sequentially webbed spaces |
| title_short | Mackey convergence and quasi-sequentially webbed spaces |
| title_sort | mackey convergence and quasi sequentially webbed spaces |
| topic | webbed space quasi-sequentially webbed space Mackey convergence fast convergence local completeness inductive limit. |
| url | http://dx.doi.org/10.1155/S0161171291000029 |
| work_keys_str_mv | AT thomasegilsdorf mackeyconvergenceandquasisequentiallywebbedspaces |