Realcompactifications of frames

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dc.contributor.advisorGilmour, Christopher Robert Andersonen_ZA
dc.contributor.authorMarcus, Nizaren_ZA
dc.date.accessioned2015-10-28T05:29:53Z
dc.date.available2015-10-28T05:29:53Z
dc.date.issued1993en_ZA
dc.descriptionBibliography: leaves 53-57.en_ZA
dc.description.abstractThe first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications.en_ZA
dc.identifier.apacitationMarcus, N. (1993). <i>Realcompactifications of frames</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/14380en_ZA
dc.identifier.chicagocitationMarcus, Nizar. <i>"Realcompactifications of frames."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993. http://hdl.handle.net/11427/14380en_ZA
dc.identifier.citationMarcus, N. 1993. Realcompactifications of frames. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Marcus, Nizar AB - The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications. DA - 1993 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1993 T1 - Realcompactifications of frames TI - Realcompactifications of frames UR - http://hdl.handle.net/11427/14380 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/14380
dc.identifier.vancouvercitationMarcus N. Realcompactifications of frames. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/14380en_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.otherframeen_ZA
dc.subject.otherσ-frameen_ZA
dc.subject.otherrealcompactificationen_ZA
dc.titleRealcompactifications of framesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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