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Hyperconvex hulls in catergories of quasi-metric spaces
Includes bibliographical references.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613208783618048 |
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| access_status_str | Open Access |
| author | Agyingi, Collins Amburo |
| author2 | Künzi, Hans-Peter A |
| author_browse | Agyingi, Collins Amburo Künzi, Hans-Peter A |
| author_facet | Künzi, Hans-Peter A Agyingi, Collins Amburo |
| author_sort | Agyingi, Collins Amburo |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/12708 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:29.432Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| 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:11427/12708 Hyperconvex hulls in catergories of quasi-metric spaces Agyingi, Collins Amburo Künzi, Hans-Peter A Includes bibliographical references. Isbell showed that every metric space has an injective hull, that is, every metric space has a “minimal” hyperconvex metric superspace. Dress then showed that the hyperconvex hull is a tight extension. In analogy to Isbell’s theory Kemajou et al. proved that each T₀-quasi-metric space X has a q-hyperconvex hull QX , which is joincompact if X is joincompact. They called a T₀-quasi-metric space q-hyperconvex if and only if it is injective in the category of T₀-quasi-metric spaces and non-expansive maps. Agyingi et al. generalized results due to Dress on tight extensions of metric spaces to the category of T₀-quasi-metric spaces and non-expansive maps. In this dissertation, we shall study tight extensions (called uq-tight extensions in the following) in the categories of T₀-quasi-metric spaces and T₀-ultra-quasimetric spaces. We show in particular that most of the results stay the same as we move from T₀-quasi-metric spaces to T₀-ultra-quasi-metric spaces. We shall show that these extensions are maximal among the uq-tight extensions of the space in question. In the second part of the dissertation we shall study the q-hyperconvex hull by viewing it as a space of minimal function pairs. We will also consider supseparability of the space of minimal function pairs. Furthermore we study a special subcollection of bicomplete supseparable quasi-metric spaces: bicomplete supseparable ultra-quasi-metric spaces. We will show the existence and uniqueness (up to isometry) of a Urysohn Γ-ultra-quasi-metric space, for an arbitrary countable set Γ of non-negative real numbers including 0. 2015-05-04T07:04:08Z 2015-05-04T07:04:08Z 2014 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/12708 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Agyingi, Collins Amburo Hyperconvex hulls in catergories of quasi-metric spaces |
| thesis_degree_str | Doctoral |
| title | Hyperconvex hulls in catergories of quasi-metric spaces |
| title_full | Hyperconvex hulls in catergories of quasi-metric spaces |
| title_fullStr | Hyperconvex hulls in catergories of quasi-metric spaces |
| title_full_unstemmed | Hyperconvex hulls in catergories of quasi-metric spaces |
| title_short | Hyperconvex hulls in catergories of quasi-metric spaces |
| title_sort | hyperconvex hulls in catergories of quasi metric spaces |
| url | http://hdl.handle.net/11427/12708 |
| work_keys_str_mv | AT agyingicollinsamburo hyperconvexhullsincatergoriesofquasimetricspaces |