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Hyperconvexity and endpoints in T₀-quasi-metric spaces
Over the last decades much progress has been made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. Th...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613690211074048 |
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| access_status_str | Open Access |
| author | Haihambo, Paulus |
| author2 | Künzi, Hans-Peter A |
| author_browse | Haihambo, Paulus Künzi, Hans-Peter A |
| author_facet | Künzi, Hans-Peter A Haihambo, Paulus |
| author_sort | Haihambo, Paulus |
| collection | Thesis |
| description | Over the last decades much progress has been made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. The aim of this dissertation is to begin an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. It starts off with basic definitions and some well-known properties of quasi-pseudometric spaces. We conclude by commencing an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. In this dissertation several results obtained for hyperconvexity and endpoints in metric spaces are generalized to T₀-quasi-metric spaces, and some original results for hyperconvexity and endpoints of T₀-quasi-metric spaces are presented. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T₀-quasi-metric space. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/6617 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:40:09.323Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| 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:11427/6617 Hyperconvexity and endpoints in T₀-quasi-metric spaces Haihambo, Paulus Künzi, Hans-Peter A Over the last decades much progress has been made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. The aim of this dissertation is to begin an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. It starts off with basic definitions and some well-known properties of quasi-pseudometric spaces. We conclude by commencing an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. In this dissertation several results obtained for hyperconvexity and endpoints in metric spaces are generalized to T₀-quasi-metric spaces, and some original results for hyperconvexity and endpoints of T₀-quasi-metric spaces are presented. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T₀-quasi-metric space. 2014-08-20T19:08:11Z 2014-08-20T19:08:11Z 2013 Master Thesis Masters MSc http://hdl.handle.net/11427/6617 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Haihambo, Paulus Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| thesis_degree_str | Master's |
| title | Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| title_full | Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| title_fullStr | Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| title_full_unstemmed | Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| title_short | Hyperconvexity and endpoints in T₀-quasi-metric spaces |
| title_sort | hyperconvexity and endpoints in t₀ quasi metric spaces |
| url | http://hdl.handle.net/11427/6617 |
| work_keys_str_mv | AT haihambopaulus hyperconvexityandendpointsint0quasimetricspaces |