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Construction of quasi-metrics determined by orders
The second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, man...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613755647459328 |
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| access_status_str | Open Access |
| author | Gaba, Yae O K Ulrich |
| author2 | Künzi, Hans-Peter A |
| author_browse | Gaba, Yae O K Ulrich Künzi, Hans-Peter A |
| author_facet | Künzi, Hans-Peter A Gaba, Yae O K Ulrich |
| author_sort | Gaba, Yae O K Ulrich |
| collection | Thesis |
| description | The second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology have been done in order to extend known results of the classical theory. It is the aim of this thesis to dig more into this theory by investigating the existence of quasi-pseudometrics that produce a given partially ordered metric space. We show that whenever one has an ordered metric space, it is often possible to describe both the metric and the order using quasi-pseudometrics. We establish respectively topological and algebraic conditions for the existence of such quasi-pseudometrics.We deduct some specific conditions when the ordered metric space(X; m,≤) is assumed to have some topological properties such as compactness. When a producing quasi-pseudo metric exists, the question of uniqueness is also studied. A characterization of produced spaces is given. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/20769 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:41:11.728Z |
| 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:11427/20769 Construction of quasi-metrics determined by orders Gaba, Yae O K Ulrich Künzi, Hans-Peter A Mathematics and Applied Mathematics The second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology have been done in order to extend known results of the classical theory. It is the aim of this thesis to dig more into this theory by investigating the existence of quasi-pseudometrics that produce a given partially ordered metric space. We show that whenever one has an ordered metric space, it is often possible to describe both the metric and the order using quasi-pseudometrics. We establish respectively topological and algebraic conditions for the existence of such quasi-pseudometrics.We deduct some specific conditions when the ordered metric space(X; m,≤) is assumed to have some topological properties such as compactness. When a producing quasi-pseudo metric exists, the question of uniqueness is also studied. A characterization of produced spaces is given. 2016-07-26T12:15:29Z 2016-07-26T12:15:29Z 2016 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/20769 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Gaba, Yae O K Ulrich Construction of quasi-metrics determined by orders |
| thesis_degree_str | Doctoral |
| title | Construction of quasi-metrics determined by orders |
| title_full | Construction of quasi-metrics determined by orders |
| title_fullStr | Construction of quasi-metrics determined by orders |
| title_full_unstemmed | Construction of quasi-metrics determined by orders |
| title_short | Construction of quasi-metrics determined by orders |
| title_sort | construction of quasi metrics determined by orders |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/20769 |
| work_keys_str_mv | AT gabayaeokulrich constructionofquasimetricsdeterminedbyorders |