Generalised sequences and compactness notions in point-free topology

Masuret, Jacques (2017-12)

Thesis (PhD)--Stellenbosch University, 2017

Thesis

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".

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/102704
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