(Stellenbosch : Stellenbosch University, 2017-12) Masuret, Jacques; Holgate, D; Sioen, M; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences.
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.