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Uniform sigma frames and the cozero part of uniform frames
In this thesis some general results on uniform frames are established and then, after defining a 'uniform sigma frame', the correspondence between the two is explored via the 'uniform cozero part' of a uniform frame. It is shown that the Lindelof uniform frames and the uniform sigma frames are in fa...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613344172605440 |
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| access_status_str | Open Access |
| author | Walters, J L |
| author2 | Gilmour, Christopher Robert Anderson |
| author_browse | Gilmour, Christopher Robert Anderson Walters, J L |
| author_facet | Gilmour, Christopher Robert Anderson Walters, J L |
| author_sort | Walters, J L |
| collection | Thesis |
| description | In this thesis some general results on uniform frames are established and then, after defining a 'uniform sigma frame', the correspondence between the two is explored via the 'uniform cozero part' of a uniform frame. It is shown that the Lindelof uniform frames and the uniform sigma frames are in fact equivalent as categories, and that properties of, and constructions using separable uniform frames can be obtained by considering the uniform cozero part. For example, the Samuel compactification of a separable uniform frame can be obtained via the Samuel compactification (in the sigma frame sense) of the underlying cozero part of the uniform frame. Throughout the thesis, choice principles such as the axioms of choice and countably dependent choice, are used, and generally without mention. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18467 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:39.078Z |
| 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:11427/18467 Uniform sigma frames and the cozero part of uniform frames Walters, J L Gilmour, Christopher Robert Anderson Mathematics Lattice theory In this thesis some general results on uniform frames are established and then, after defining a 'uniform sigma frame', the correspondence between the two is explored via the 'uniform cozero part' of a uniform frame. It is shown that the Lindelof uniform frames and the uniform sigma frames are in fact equivalent as categories, and that properties of, and constructions using separable uniform frames can be obtained by considering the uniform cozero part. For example, the Samuel compactification of a separable uniform frame can be obtained via the Samuel compactification (in the sigma frame sense) of the underlying cozero part of the uniform frame. Throughout the thesis, choice principles such as the axioms of choice and countably dependent choice, are used, and generally without mention. 2016-04-01T06:46:27Z 2016-04-01T06:46:27Z 1989 Master Thesis Masters MSc http://hdl.handle.net/11427/18467 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Lattice theory Walters, J L Uniform sigma frames and the cozero part of uniform frames |
| thesis_degree_str | Master's |
| title | Uniform sigma frames and the cozero part of uniform frames |
| title_full | Uniform sigma frames and the cozero part of uniform frames |
| title_fullStr | Uniform sigma frames and the cozero part of uniform frames |
| title_full_unstemmed | Uniform sigma frames and the cozero part of uniform frames |
| title_short | Uniform sigma frames and the cozero part of uniform frames |
| title_sort | uniform sigma frames and the cozero part of uniform frames |
| topic | Mathematics Lattice theory |
| url | http://hdl.handle.net/11427/18467 |
| work_keys_str_mv | AT waltersjl uniformsigmaframesandthecozeropartofuniformframes |