Text in English / Submitted in partial fulfillment of a Master's Degree at the University of South Africa / Our main goal is to collate into a single document what is presently known regarding pointfree convergence. This will be done by exposing some well-known results on pointfree convergence in a much more simpler way. We will start to study the convergence and clustering of filters in frames in terms of covers and use this to characterise compact frames and some type of uniform frames. We will extend this study to a more general type of filters. We will then discuss convergence and clustering of filters on a locale, where a filter on a locale L is just a filter in the sublattice of all
the sublocales of L. This convergence has many applications like characterising compact locales
and also characterising sharp points which will also be studied. Finally, the latter concepts of
convergence and clustering will be reconciled with the previous one. / Mathematical Sciences
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/25922 |
| Date | 01 1900 |
| Creators | Ngo Babem, Annette Flavie |
| Contributors | Dube, Themba |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
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