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Metrization of ordered topological spaces
In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions nece...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613174447996928 |
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| access_status_str | Open Access |
| author | Colquhoun, Alan |
| author2 | Salbany, Sergio de Ornelas |
| author_browse | Colquhoun, Alan Salbany, Sergio de Ornelas |
| author_facet | Salbany, Sergio de Ornelas Colquhoun, Alan |
| author_sort | Colquhoun, Alan |
| collection | Thesis |
| description | In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions necessary for metrizability of such spaces. One of the earliest papers concerned with ordered topological spaces is that of Eilenberg. Since then, ordered spaces have been considered by various authors, but few considered the conditions under which such spaces would be metrizable. Bennet gave a characterization of metrizability for a linearly ordered topological space with a σ-point finite base. A linearly ordered topological space is a space for which the interval topology coincides with the original topology for the space. We investigate the metrizability of linearly ordered topological space satisfying certain covering properties, countability conditions on the base, certain conditions on the diagonal and spaces which admit a symmetric. We obtain four characterizations of metrizability for linearly ordered topological space in terms of some of the above notions. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17677 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:56.645Z |
| 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:11427/17677 Metrization of ordered topological spaces Colquhoun, Alan Salbany, Sergio de Ornelas Applied Mathematics Topology In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions necessary for metrizability of such spaces. One of the earliest papers concerned with ordered topological spaces is that of Eilenberg. Since then, ordered spaces have been considered by various authors, but few considered the conditions under which such spaces would be metrizable. Bennet gave a characterization of metrizability for a linearly ordered topological space with a σ-point finite base. A linearly ordered topological space is a space for which the interval topology coincides with the original topology for the space. We investigate the metrizability of linearly ordered topological space satisfying certain covering properties, countability conditions on the base, certain conditions on the diagonal and spaces which admit a symmetric. We obtain four characterizations of metrizability for linearly ordered topological space in terms of some of the above notions. 2016-03-14T07:03:48Z 2016-03-14T07:03:48Z 1974 Master Thesis Masters MSc http://hdl.handle.net/11427/17677 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Topology Colquhoun, Alan Metrization of ordered topological spaces |
| thesis_degree_str | Master's |
| title | Metrization of ordered topological spaces |
| title_full | Metrization of ordered topological spaces |
| title_fullStr | Metrization of ordered topological spaces |
| title_full_unstemmed | Metrization of ordered topological spaces |
| title_short | Metrization of ordered topological spaces |
| title_sort | metrization of ordered topological spaces |
| topic | Applied Mathematics Topology |
| url | http://hdl.handle.net/11427/17677 |
| work_keys_str_mv | AT colquhounalan metrizationoforderedtopologicalspaces |