On localic convergence with applications

Ngo Babem, Annette Flavie

dc.contributor.advisor	Dube, Themba
dc.contributor.author	Ngo Babem, Annette Flavie
dc.date.accessioned	2019-11-01T13:31:31Z
dc.date.available	2019-11-01T13:31:31Z
dc.date.issued	2019-01
dc.identifier.uri	http://hdl.handle.net/10500/25922
dc.description	Text in English	en
dc.description	Submitted in partial fulfillment of a Master's Degree at the University of South Africa
dc.description.abstract	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.	en
dc.language.iso	en	en
dc.subject	Uniform frame	en
dc.subject	Compact locale	en
dc.subject	Sublocale	en
dc.subject	Convergent filter in a frame	en
dc.subject	Clustered filter in a frame	en
dc.subject	General filter on a frame	en
dc.subject	F-compact frame	en
dc.subject	Convergent filter on a locale	en
dc.subject	Clustered filter on a locale	en
dc.subject	Sharp point	en
dc.subject.ddc	514.3
dc.subject.lcsh	Topology
dc.title	On localic convergence with applications	en
dc.type	Dissertation	en
dc.description.department	Mathematical Sciences	en