{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/38321"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/38321","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Local connectedness of frames","abstract":"In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5.","abstract_html":"In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5.","abstract_has_math":false,"creators":["Mushaandja, Zechariah"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Schauerte, Anneliese"],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:22:41Z","subjects":["mathematics and applied mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/38321","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Schauerte, Anneliese"]},{"key":"dc:creator","label":"Author","values":["Mushaandja, Zechariah"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-08-29T11:40:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-08-29T11:40:15Z"]},{"key":"dc:date.issued","label":"Date","values":["2004"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MSc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematics and applied mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/38321"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5."]},{"key":"dc:title","label":"Title","values":["Local connectedness of frames"]}]}],"canonical_facts":{"dc:contributor.advisor":["Schauerte, Anneliese"],"dc:creator":["Mushaandja, Zechariah"],"dc:date.accessioned":["2023-08-29T11:40:15Z"],"dc:date.available":["2023-08-29T11:40:15Z"],"dc:date.issued":["2004"],"dc:description.abstract":["In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5."],"dc:identifier.uri":["http://hdl.handle.net/11427/38321"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["mathematics and applied mathematics"],"dc:title":["Local connectedness of frames"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters","MSc"]},"updated_at":"2026-07-22T22:22:41Z"}