Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Stability of barrelled topologies
Bibliography: leaf 86-88.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2016
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613232958537728 |
|---|---|
| access_status_str | Open Access |
| author | Burton, Michael Howard |
| author2 | Webb, John H |
| author_browse | Burton, Michael Howard Webb, John H |
| author_facet | Webb, John H Burton, Michael Howard |
| author_sort | Burton, Michael Howard |
| collection | Thesis |
| description | Bibliography: leaf 86-88. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/16974 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:52.713Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/16974 Stability of barrelled topologies Burton, Michael Howard Webb, John H Mathematics Bibliography: leaf 86-88. In the theory of locally convex topological vector spaces, barrelled topologies have been found to be stable under the formation of products, sums and quotients. We shall in this thesis investigate the stability of barrelled topologies with respect to two further mathematical constructions. Firstly, we examine the situation with regard to the formation of finite-codimensional and countable-codimensional subspaces. (Of course, barrelled topologies are not stable under the formation of arbitrary subspaces.) Secondly, we present what is known about the stability of barrelled topologies with respect to enlargements of the dual space - a concept which is defined in the sequel. This aspect of the stability question was tackled in a recent paper by Robertson and Yeomans and was pursued in two subsequent papers by Tweddle and Yeomans and by Robertson, Tweddle and Yeomans. In the next two chapters, we turn our attention to quasibarrelled topologies and we pursue a parallel investigation to that of the first two chapters. Finally we conduct a similar investigation on σ-barrelled and σ-quasibarrelled spaces. The results 5.2, 5.3, 5.4, 5.5, 5.6, 6.2, 6.3, 6.4 and 6.5 concerning these spaces are original. 2016-02-12T07:12:40Z 2016-02-12T07:12:40Z 1983 Master Thesis Masters MSc http://hdl.handle.net/11427/16974 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Burton, Michael Howard Stability of barrelled topologies |
| thesis_degree_str | Master's |
| title | Stability of barrelled topologies |
| title_full | Stability of barrelled topologies |
| title_fullStr | Stability of barrelled topologies |
| title_full_unstemmed | Stability of barrelled topologies |
| title_short | Stability of barrelled topologies |
| title_sort | stability of barrelled topologies |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/16974 |
| work_keys_str_mv | AT burtonmichaelhoward stabilityofbarrelledtopologies |