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Neighbourhood operators on Categories
Thesis (PhD)--Stellenbosch University, 2013.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2013
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| _version_ | 1867613974667722752 |
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| access_status_str | Open Access |
| author | Razafindrakoto, Ando Desire |
| author2 | Holgate, David B. |
| author_browse | Holgate, David B. Razafindrakoto, Ando Desire |
| author_facet | Holgate, David B. Razafindrakoto, Ando Desire |
| author_sort | Razafindrakoto, Ando Desire |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2013. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/80169 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:44:39.798Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/80169 Neighbourhood operators on Categories Razafindrakoto, Ando Desire Holgate, David B. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Topological spaces Categories (Mathematics) 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. Doctoral 2013-02-26T16:38:04Z 2013-03-15T07:38:46Z 2013-02-26T16:38:04Z 2013-03-15T07:38:46Z 2013-03 Thesis http://hdl.handle.net/10019.1/80169 en_ZA Stellenbosch University 87 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Topological spaces Categories (Mathematics) Razafindrakoto, Ando Desire Neighbourhood operators on Categories |
| title | Neighbourhood operators on Categories |
| title_full | Neighbourhood operators on Categories |
| title_fullStr | Neighbourhood operators on Categories |
| title_full_unstemmed | Neighbourhood operators on Categories |
| title_short | Neighbourhood operators on Categories |
| title_sort | neighbourhood operators on categories |
| topic | Topological spaces Categories (Mathematics) |
| url | http://hdl.handle.net/10019.1/80169 |
| work_keys_str_mv | AT razafindrakotoandodesire neighbourhoodoperatorsoncategories |