On the collection of topologies, generalised metrics and continuity spaces

Abstract

This article-based thesis comprises a collection of four papers, each of which constitutes a chapter written in manuscript form. The elemental theme behind the first three chapters is the study of several collections of (topological) structures on an arbitrary set. A more holistic and unifying view of these structures is given in Chapter 4 where a categorical approach is taken and the individuality of fixing a set is abandoned.