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Neighbourhood operators on Categories

dc.contributor.advisorHolgate, David B.en_ZA
dc.contributor.authorRazafindrakoto, Ando Desireen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2013-02-26T16:38:04Zen_ZA
dc.date.accessioned2013-03-15T07:38:46Z
dc.date.available2013-02-26T16:38:04Zen_ZA
dc.date.available2013-03-15T07:38:46Z
dc.date.issued2013-03en_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/80169
dc.descriptionThesis (PhD)--Stellenbosch University, 2013.en_ZA
dc.description.abstractENGLISH ABSTRACT: While the notions of open and closed subsets in a topological space are dual to each other, they take on another meaning when points and complements are no longer available. Closure operators have been extensively used to study topological notions on categories. Though this has recovered a fair amount of topological results and has brought an economy of e ort and insight into Topology, it is thought that certain properties, such as convergence, are naturally associated with neighbourhoods. On the other hand, it is interesting enough to investigate certain notions, such as that of closed maps, which in turn are naturally associated with closure by means of neighbourhoods. We propose in this thesis a set of axioms for neighbourhoods and test them with the properties of connectedness and compactness.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Al is die twee konsepte van oop en geslote subversamelings in 'n topologiese ruimte teenoorgesteldes van mekaar, verander hul betekenis wanneer punte en komplemente nie meer ter sprake is nie. Die gebruik van afsluitingsoperatore is alreeds omvattend in die studie van topologiese konsepte in kategorieë, toegepas. Alhoewel 'n redelike aantal topologiese resultate, groeiende belangstelling en groter insig tot Topologie die gevolg was, word daar geglo dat seker eienskappe, soos konvergensie, op 'n natuurlike wyse aan omgewings verwant is. Nietemin is dit van belang om sekere eienskappe, soos geslote afbeeldings, wat natuurlik verwant is aan afsluiting, te bestudeer. In hierdie proefskrif stel ons 'n aantal aksiomas oor omgewings voor en toets dit gevolglik met die eienskappe van samehangendheid en kompaktheid.af_ZA
dc.format.extent87 p.
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.subjectTopological spacesen_ZA
dc.subjectCategories (Mathematics)en_ZA
dc.titleNeighbourhood operators on Categoriesen_ZA
dc.typeThesisen_ZA
dc.rights.holderStellenbosch Universityen_ZA


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