Uniform sigma frames and the cozero part of uniform frames

In this thesis some general results on uniform frames are established and then, after defining a 'uniform sigma frame', the correspondence between the two is explored via the 'uniform cozero part' of a uniform frame. It is shown that the Lindelof uniform frames and the uniform sigma frames are in fact equivalent as categories, and that properties of, and constructions using separable uniform frames can be obtained by considering the uniform cozero part. For example, the Samuel compactification of a separable uniform frame can be obtained via the Samuel compactification (in the sigma frame sense) of the underlying cozero part of the uniform frame. Throughout the thesis, choice principles such as the axioms of choice and countably dependent choice, are used, and generally without mention.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1989

Author dc:creator

• Walters, J L

Advisor dc:contributor.advisor

• Gilmour, Christopher Robert Anderson

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/18467

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/18467