Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH 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. / AFRIKAANSE 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/80169 |
| Date | 03 1900 |
| Creators | Razafindrakoto, Ando Desire |
| Contributors | Holgate, David B., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 87 p. |
| Rights | Stellenbosch University |
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