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(Strongly) zero-dimensional ordered spaces
Includes bibliographical references.
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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_ | 1867614046520344576 |
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| access_status_str | Open Access |
| author | Nailana, Kwena Rufus |
| author2 | Brümmer, Guillaume C L |
| author_browse | Brümmer, Guillaume C L Nailana, Kwena Rufus |
| author_facet | Brümmer, Guillaume C L Nailana, Kwena Rufus |
| author_sort | Nailana, Kwena Rufus |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17403 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:45:49.126Z |
| 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:11427/17403 (Strongly) zero-dimensional ordered spaces Nailana, Kwena Rufus Brümmer, Guillaume C L Mathematics Topology Includes bibliographical references. The relationship between transitive uniform spaces and zero-dimensional topological spaces was first established by Banaschewski [1957], and was later investigated by Levine [1969]. The theory of transitive quasi-uniform spaces is treated in [Fletcher and Lindgren 1972], [Brummer 1984] and [Kiinzi 1990, 1992a, 1992b,1993]; a convenient presentation for our purpose is to be found in [Fletcher and Lindgren 1982]. After Reilly [1972] introduced the notion of zero-dimensionality in bitopological spaces, Birsan [1974] and Halpin [1974] studied the relationship between transitive quasi-uniform spaces and zero-dimensional bitopological spaces. In this thesis we define a notion of zero-dimensionality in ordered topological spaces and examine the relationship between transitive quasi-uniform spaces and zero-dimensional ordered topological spaces. To a large extent, our presentation is influenced by the situation in bitopological spaces (cf. [Halpin 1974] and [Birsan 1974]), and uses the commutative diagrams which occur in [Schauerte 1988] and [Brummer 1977, 1982]. We also study strongly zero-dimensional ordered topological spaces and their relation with functorial quasi-uniformities. In this respect, our results are influenced by those of [Fora 1984], [Banaschewski and Brummer 1990] and [Kiinzi 1990] for strongly zero-dimensional bitopological spaces. 2016-03-01T07:44:11Z 2016-03-01T07:44:11Z 1993 Master Thesis Masters MSc http://hdl.handle.net/11427/17403 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Topology Nailana, Kwena Rufus (Strongly) zero-dimensional ordered spaces |
| thesis_degree_str | Master's |
| title | (Strongly) zero-dimensional ordered spaces |
| title_full | (Strongly) zero-dimensional ordered spaces |
| title_fullStr | (Strongly) zero-dimensional ordered spaces |
| title_full_unstemmed | (Strongly) zero-dimensional ordered spaces |
| title_short | (Strongly) zero-dimensional ordered spaces |
| title_sort | strongly zero dimensional ordered spaces |
| topic | Mathematics Topology |
| url | http://hdl.handle.net/11427/17403 |
| work_keys_str_mv | AT nailanakwenarufus stronglyzerodimensionalorderedspaces |