Normal bases and compactifications of frames - Robertson, Angela May (Department of Mathematics and Applied Mathematics, 2016)
The initial aim of this dissertation was to provide a frame-theoretic analogue of Banaschewski's normal systems of sets in [5] as well as a frame counterpart to their associated compactifications. Having completed this part of the task, it seemed natural to investigate the relationship between this compactification and those mentioned above. Hence the first five chapters of the dissertation are devoted to the study of the frame counterparts to six well-known compactifications in the category of topological spaces. For each compactification studied, we give some motivation as to why it should be regarded as a frame-theoretic analogue of its classical counterpart. The sixth chapter is concerned with the relationships between the compactifications: in particular we are interested in conditions under which the different constructions give rise to the same compactification.