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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Main Author: Robertson, Angela May
Other Authors: Gilmour, Christopher Robert Anderson
Format: Dissertation
Language:English
Published: University of Cape Town 2016
Subjects:
Online Access:http://hdl.handle.net/11427/18247
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spelling 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
collection NDLTD
language English
format Dissertation
sources NDLTD
topic Mathematics
spellingShingle 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
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