{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/18467"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/18467","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Uniform sigma frames and the cozero part of uniform frames","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Walters, J L"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gilmour, Christopher Robert Anderson"],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989","date_published":"1989","updated_at":"2026-07-22T22:23:29Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/18467","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gilmour, Christopher Robert Anderson"]},{"key":"dc:creator","label":"Author","values":["Walters, J L"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-04-01T06:46:27Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-01T06:46:27Z"]},{"key":"dc:date.issued","label":"Date","values":["1989"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/18467"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Uniform sigma frames and the cozero part of uniform frames"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gilmour, Christopher Robert Anderson"],"dc:creator":["Walters, J L"],"dc:date.accessioned":["2016-04-01T06:46:27Z"],"dc:date.available":["2016-04-01T06:46:27Z"],"dc:date.issued":["1989"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/18467"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Uniform sigma frames and the cozero part of uniform frames"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:29Z"}