E-compactness in pointfree topology

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dc.contributor.advisorGilmour, Christopher Robert Andersonen_ZA
dc.contributor.authorMarcus, Nizaren_ZA
dc.date.accessioned2014-11-11T20:11:33Z
dc.date.available2014-11-11T20:11:33Z
dc.date.issued1998en_ZA
dc.descriptionBibliography: leaves 100-107.en_ZA
dc.description.abstractThe 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.identifier.apacitationMarcus, N. (1998). <i>E-compactness in pointfree topology</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/9572en_ZA
dc.identifier.chicagocitationMarcus, Nizar. <i>"E-compactness in pointfree topology."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998. http://hdl.handle.net/11427/9572en_ZA
dc.identifier.citationMarcus, N. 1998. E-compactness in pointfree topology. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Marcus, Nizar AB - 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. DA - 1998 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1998 T1 - E-compactness in pointfree topology TI - E-compactness in pointfree topology UR - http://hdl.handle.net/11427/9572 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/9572
dc.identifier.vancouvercitationMarcus N. E-compactness in pointfree topology. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9572en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleE-compactness in pointfree topologyen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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