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Generalised sequences and compactness notions in point-free topology
Thesis (PhD)--Stellenbosch University, 2017
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2017
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| _version_ | 1867614139689467904 |
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| access_status_str | Open Access |
| author | Masuret, Jacques |
| author2 | Holgate, D |
| author_browse | Holgate, D Masuret, Jacques |
| author_facet | Holgate, D Masuret, Jacques |
| author_sort | Masuret, Jacques |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2017 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/102704 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:47:17.937Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/102704 Generalised sequences and compactness notions in point-free topology Masuret, Jacques Holgate, D Sioen, M Stellenbosch University. Faculty of Science. Department of Mathematical Sciences. Generalized sequence (Mathematics) Convergence (Mathematics) Point-free topology Dini's theorem UCTD Algebra, Boolean Topology Thesis (PhD)--Stellenbosch University, 2017 ENGLISH 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. AFRIKAANSE 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". Doctoral 2017-09-13T11:21:06Z 2017-12-11T10:43:45Z 2017-09-13T11:21:06Z 2017-12-11T10:43:45Z 2017-12 Thesis http://hdl.handle.net/10019.1/102704 en_ZA Stellenbosch University viii, 110 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Generalized sequence (Mathematics) Convergence (Mathematics) Point-free topology Dini's theorem UCTD Algebra, Boolean Topology Masuret, Jacques Generalised sequences and compactness notions in point-free topology |
| title | Generalised sequences and compactness notions in point-free topology |
| title_full | Generalised sequences and compactness notions in point-free topology |
| title_fullStr | Generalised sequences and compactness notions in point-free topology |
| title_full_unstemmed | Generalised sequences and compactness notions in point-free topology |
| title_short | Generalised sequences and compactness notions in point-free topology |
| title_sort | generalised sequences and compactness notions in point free topology |
| topic | Generalized sequence (Mathematics) Convergence (Mathematics) Point-free topology Dini's theorem UCTD Algebra, Boolean Topology |
| url | http://hdl.handle.net/10019.1/102704 |
| work_keys_str_mv | AT masuretjacques generalisedsequencesandcompactnessnotionsinpointfreetopology |