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Separability and metrisability in locally convex spaces
Bibliography: pages 58-61.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613259024039936 |
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| access_status_str | Open Access |
| author | Robertson, Neill Raymond Charles |
| author2 | Webb, John H |
| author_browse | Robertson, Neill Raymond Charles Webb, John H |
| author_facet | Webb, John H Robertson, Neill Raymond Charles |
| author_sort | Robertson, Neill Raymond Charles |
| collection | Thesis |
| description | Bibliography: pages 58-61. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/21966 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:17.409Z |
| 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:11427/21966 Separability and metrisability in locally convex spaces Robertson, Neill Raymond Charles Webb, John H Mathematics and Applied Mathematics Bibliography: pages 58-61. This thesis is devoted to a study of the relationship between separability and metrisability in the context of locally convex spaces. The duality between sep- arability and weak*-metrisability does not carry over to non-metrisable locally convex spaces; the best that can be said in this case is that the equicontinuous subsets in the dual of a separable locally convex space are weak*-metrisable. To get around this difficulty, we often prefer to use the idea of separability by seminorm: a locally convex space E is separable by seminorm if and only if the equicontinuous subsets of its dual are weak*-metrisable. On any locally convex space E there is a finest topology Tχ which is coarser than the given topology and which makes E separable by seminorm. A question that arises is under what conditions a space E is Tχ-complete. In trying to answer this question, we are led to an intriguing binary relation which G.A. Edgar originally defined on the class of Banach spaces. In the first two Chapters of this thesis, we show that many of the results in Edgar's paper can be expressed in terms of the completeness of a space with respect to various topologies. 2016-09-28T18:59:39Z 2016-09-28T18:59:39Z 1991 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/21966 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Robertson, Neill Raymond Charles Separability and metrisability in locally convex spaces |
| thesis_degree_str | Doctoral |
| title | Separability and metrisability in locally convex spaces |
| title_full | Separability and metrisability in locally convex spaces |
| title_fullStr | Separability and metrisability in locally convex spaces |
| title_full_unstemmed | Separability and metrisability in locally convex spaces |
| title_short | Separability and metrisability in locally convex spaces |
| title_sort | separability and metrisability in locally convex spaces |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/21966 |
| work_keys_str_mv | AT robertsonneillraymondcharles separabilityandmetrisabilityinlocallyconvexspaces |