Generalised sequences and compactness notions in point-free topology

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dc.contributor.advisorHolgate, Den_ZA
dc.contributor.advisorSioen, Men_ZA
dc.contributor.authorMasuret, Jacquesen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Department of Mathematical Sciences.en_ZA
dc.date.accessioned2017-09-13T11:21:06Z
dc.date.accessioned2017-12-11T10:43:45Z
dc.date.available2017-09-13T11:21:06Z
dc.date.available2017-12-11T10:43:45Z
dc.date.issued2017-12
dc.descriptionThesis (PhD)--Stellenbosch University, 2017en_ZA
dc.description.abstractENGLISH ABSTRACT : While sequences and naturally associated notions like convergence and clustering have received extensive attention in classical topology, the same cannot be said for the point-free setting. The aim of this dissertation is to introduce sequences and related sequential notions in frames and to establish the extent to which point-free sequences can characterise countable compactness notions. Furthermore, we will introduce the point-free Dini Property and Strong Dini Property and employ these properties to characterise weaker compactness notions. We also characterise those completely regular frames satisfying the Stone-Weierstrass property.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING : Terwyl rye en natuurlike geassosieerde konsepte soos konvergensie en groepering "clustering" omvattende aandag in klassieke topologie geniet het, kan dieselfde nie vir die puntvrye omgewing gesê word nie. Die doel van hierdie proefskrif is om veralgemeende rye en vewante konsepte in te voer en vas te stel tot watter mate hierdie puntvrye rye aftelbare vorme van kompaktheid kan karakteriseer. Daarbenewens sal ons die puntvrye Dini Eienskap "Dini Property" en Sterk Dini Eienskap "Strong Dini Property" ondersoek en swakker vorme van kompaktheid daarmee karakteriseer. Ons karakteriseer ook die volledig reguliere puntvrye ruimtes met die Stone-Weierstrass Eienskap "Stone-Weierstrass Property".af_ZA
dc.format.extentviii, 110 pagesen_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/102704
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectGeneralized sequence (Mathematics)en_ZA
dc.subjectConvergence (Mathematics)en_ZA
dc.subjectPoint-free topologyen_ZA
dc.subjectDini's theoremen_ZA
dc.subjectUCTDen_ZA
dc.subjectAlgebra, Booleanen_ZA
dc.subjectTopologyen_ZA
dc.titleGeneralised sequences and compactness notions in point-free topologyen_ZA
dc.typeThesisen_ZA
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