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...
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ndltd-netd.ac.za-oai-union.ndltd.org-uct-oai-localhost-11427-182472020-10-06T05:10:53Z 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 University of Cape Town Faculty of Science Department of Mathematics and Applied Mathematics |
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English |
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Dissertation |
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Mathematics |
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Mathematics Robertson, Angela May Normal bases and compactifications of frames |
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. |
author2 |
Gilmour, Christopher Robert Anderson |
author_facet |
Gilmour, Christopher Robert Anderson Robertson, Angela May |
author |
Robertson, Angela May |
author_sort |
Robertson, Angela May |
title |
Normal bases and compactifications of frames |
title_short |
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_sort |
normal bases and compactifications of frames |
publisher |
University of Cape Town |
publishDate |
2016 |
url |
http://hdl.handle.net/11427/18247 |
work_keys_str_mv |
AT robertsonangelamay normalbasesandcompactificationsofframes |
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1719347744546488320 |