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E-compactness in pointfree topology
Bibliography: leaves 100-107.
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2014
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| _version_ | 1867613302177136640 |
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| access_status_str | Open Access |
| author | Marcus, Nizar |
| author2 | Gilmour, Christopher Robert Anderson |
| author_browse | Gilmour, Christopher Robert Anderson Marcus, Nizar |
| author_facet | Gilmour, Christopher Robert Anderson Marcus, Nizar |
| author_sort | Marcus, Nizar |
| collection | Thesis |
| description | Bibliography: leaves 100-107. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/9572 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:59.204Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| 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:11427/9572 E-compactness in pointfree topology Marcus, Nizar Gilmour, Christopher Robert Anderson Mathematics Bibliography: leaves 100-107. The main purpose of this thesis is to develop a point-free notion of E-compactness. Our approach follows that of Banascheski and Gilmour in [17]. Any regular frame E has a fine nearness and hence induces a nearness on an E-regular frame L. We show that the frame L is complete with respect this nearness iff L is a closed quotient of a copower of E. This resembles the classical definition, but it is not a conservative definition: There are spaces that may be embedded as closed subspaces of powers of a space E, but their frame of opens are not closed quotients of copowers of the frame of opens of E. A conservative definition of E-compactness is obtained by considering Cauchy completeness with respect to this nearness. Another central notion in the thesis is that of K-Lindelöf frames, a generalisation of Lindelöf frames introduced by J.J. Madden [59]. In the last chapter we investigate the interesting relationship between the completely regular K-Lindelöf frames and the K-compact frames. 2014-11-11T20:11:33Z 2014-11-11T20:11:33Z 1998 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/9572 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Marcus, Nizar E-compactness in pointfree topology |
| thesis_degree_str | Doctoral |
| title | E-compactness in pointfree topology |
| title_full | E-compactness in pointfree topology |
| title_fullStr | E-compactness in pointfree topology |
| title_full_unstemmed | E-compactness in pointfree topology |
| title_short | E-compactness in pointfree topology |
| title_sort | e compactness in pointfree topology |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/9572 |
| work_keys_str_mv | AT marcusnizar ecompactnessinpointfreetopology |