{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/5962"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/5962","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Nearness and convergence in pointfree topology","abstract":"We introduce and investigate the concept of a nearness structure on a σ-frame. Analogues of the Samuel Compactification, Uniform Coreflection and Completion in the nearness σ-frame setting are obtained. Convergence in uniform frames is also a subject of this thesis integrating compactness, precompactness and paracompactness. Finally, the notion of uniform paracompactness is introduced and its relation with convergence is investigated.","abstract_html":"We introduce and investigate the concept of a nearness structure on a σ-frame. Analogues of the Samuel Compactification, Uniform Coreflection and Completion in the nearness σ-frame setting are obtained. Convergence in uniform frames is also a subject of this thesis integrating compactness, precompactness and paracompactness. Finally, the notion of uniform paracompactness is introduced and its relation with convergence is investigated.","abstract_has_math":false,"creators":["Naidoo, Inderasan"],"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":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:23:12Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/5962","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":["Naidoo, Inderasan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-08-02T14:48:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-08-02T14:48:00Z"]},{"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:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"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/11427/5962"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: leaves 99-106."]},{"key":"dc:description.abstract","label":"Abstract","values":["We introduce and investigate the concept of a nearness structure on a σ-frame. Analogues of the Samuel Compactification, Uniform Coreflection and Completion in the nearness σ-frame setting are obtained. Convergence in uniform frames is also a subject of this thesis integrating compactness, precompactness and paracompactness. Finally, the notion of uniform paracompactness is introduced and its relation with convergence is investigated."]},{"key":"dc:title","label":"Title","values":["Nearness and convergence in pointfree topology"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gilmour, Christopher Robert Anderson"],"dc:creator":["Naidoo, Inderasan"],"dc:date.accessioned":["2014-08-02T14:48:00Z"],"dc:date.available":["2014-08-02T14:48:00Z"],"dc:date.issued":["2004"],"dc:description":["Bibliography: leaves 99-106."],"dc:description.abstract":["We introduce and investigate the concept of a nearness structure on a σ-frame. Analogues of the Samuel Compactification, Uniform Coreflection and Completion in the nearness σ-frame setting are obtained. Convergence in uniform frames is also a subject of this thesis integrating compactness, precompactness and paracompactness. Finally, the notion of uniform paracompactness is introduced and its relation with convergence is investigated."],"dc:identifier.uri":["http://hdl.handle.net/11427/5962"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Nearness and convergence in pointfree topology"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:12Z"}