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Normal bases and compactifications of frames
The initial aim of this dissertation was to provide a frame-theoretic analogue of Banaschewski's normal systems of sets in [5] as well as a frame counterpart to their associated compactifications. Having completed this part of the task, it seemed natural to investigate the relationship between this...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613167015690240 |
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| access_status_str | Open Access |
| author | Robertson, Angela May |
| author2 | Gilmour, Christopher Robert Anderson |
| author_browse | Gilmour, Christopher Robert Anderson Robertson, Angela May |
| author_facet | Gilmour, Christopher Robert Anderson Robertson, Angela May |
| author_sort | Robertson, Angela May |
| collection | Thesis |
| description | The initial aim of this dissertation was to provide a frame-theoretic analogue of Banaschewski's normal systems of sets in [5] as well as a frame counterpart to their associated compactifications. Having completed this part of the task, it seemed natural to investigate the relationship between this compactification and those mentioned above. Hence the first five chapters of the dissertation are devoted to the study of the frame counterparts to six well-known compactifications in the category of topological spaces. For each compactification studied, we give some motivation as to why it should be regarded as a frame-theoretic analogue of its classical counterpart. The sixth chapter is concerned with the relationships between the compactifications: in particular we are interested in conditions under which the different constructions give rise to the same compactification. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18247 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:50.330Z |
| 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:11427/18247 Normal bases and compactifications of frames Robertson, Angela May Gilmour, Christopher Robert Anderson Mathematics The initial aim of this dissertation was to provide a frame-theoretic analogue of Banaschewski's normal systems of sets in [5] as well as a frame counterpart to their associated compactifications. Having completed this part of the task, it seemed natural to investigate the relationship between this compactification and those mentioned above. Hence the first five chapters of the dissertation are devoted to the study of the frame counterparts to six well-known compactifications in the category of topological spaces. For each compactification studied, we give some motivation as to why it should be regarded as a frame-theoretic analogue of its classical counterpart. The sixth chapter is concerned with the relationships between the compactifications: in particular we are interested in conditions under which the different constructions give rise to the same compactification. 2016-03-28T14:25:42Z 2016-03-28T14:25:42Z 1995 Master Thesis Masters MSc http://hdl.handle.net/11427/18247 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Robertson, Angela May Normal bases and compactifications of frames |
| thesis_degree_str | Master's |
| title | Normal bases and compactifications of frames |
| title_full | Normal bases and compactifications of frames |
| title_fullStr | Normal bases and compactifications of frames |
| title_full_unstemmed | Normal bases and compactifications of frames |
| title_short | Normal bases and compactifications of frames |
| title_sort | normal bases and compactifications of frames |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/18247 |
| work_keys_str_mv | AT robertsonangelamay normalbasesandcompactificationsofframes |