E-compactness in pointfree topology

 

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dc.contributor.advisor Gilmour, Christopher Robert Anderson en_ZA
dc.contributor.author Marcus, Nizar en_ZA
dc.date.accessioned 2014-11-11T20:11:33Z
dc.date.available 2014-11-11T20:11:33Z
dc.date.issued 1998 en_ZA
dc.identifier.citation Marcus, N. 1998. E-compactness in pointfree topology. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/9572
dc.description Bibliography: leaves 100-107. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.title E-compactness in pointfree topology en_ZA
dc.type Thesis / Dissertation en_ZA
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Doctoral en_ZA
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
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