{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/6665"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/6665","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"On Doitchinov's quietness for arbitrary quasi-uniform spaces","abstract":"The notion of a quiet quasi-uniform space was introduced by Doitchinov in1988 when he developed an interesting completion theory for this class ofquasi-uniform spaces. At the same time Doitchinov developed a similar com-pletion theory for a class of T0-balanced quasi-pseudometric spaces.In my Masters thesis I showed that the Doitchinov completion theory forbalanced quasi-pseudometric spaces can be extended to arbitrary T0-quasi-pseudometric spaces. That completion was called the B-completion.The principal aim of this thesis is to investigate whether the Doitchinov com-pletion theory for quiet quasi-uniform space can be extended to arbitraryT0-quasi-uniform spaces. The main result in this thesis is negative and leadsus to conclude that Doitchinov's completion theory for quiet quasi-uniformspaces cannot be fully extended to arbitrary quasi-uniform spaces, becauseinvestigations due to De¶ak indicate that no suitable concept of a quiet Cauchy¯lter pair exists which could replace the quasi-pseudometric concept of a bal-anced Cauchy ¯lter pair in the quasi-uniform setting. Under these circum-stances we therefore suggest that in an arbitrary quasi-uniform space, weshould work with a nonempty subbasic family of quasi-pseudometrics and anappropriate concept of balancedness of Cauchy ¯lter pairs with respect tothat family. In this way we obtain a general theory of the B-completion fora subbasic T0-family of quasi-pseudometrics that can be applied to the studyof any quasi-uniform space.","abstract_html":"The notion of a quiet quasi-uniform space was introduced by Doitchinov in1988 when he developed an interesting completion theory for this class ofquasi-uniform spaces. At the same time Doitchinov developed a similar com-pletion theory for a class of T0-balanced quasi-pseudometric spaces.In my Masters thesis I showed that the Doitchinov completion theory forbalanced quasi-pseudometric spaces can be extended to arbitrary T0-quasi-pseudometric spaces. That completion was called the B-completion.The principal aim of this thesis is to investigate whether the Doitchinov com-pletion theory for quiet quasi-uniform space can be extended to arbitraryT0-quasi-uniform spaces. The main result in this thesis is negative and leadsus to conclude that Doitchinov's completion theory for quiet quasi-uniformspaces cannot be fully extended to arbitrary quasi-uniform spaces, becauseinvestigations due to De¶ak indicate that no suitable concept of a quiet Cauchy¯lter pair exists which could replace the quasi-pseudometric concept of a bal-anced Cauchy ¯lter pair in the quasi-uniform setting. Under these circum-stances we therefore suggest that in an arbitrary quasi-uniform space, weshould work with a nonempty subbasic family of quasi-pseudometrics and anappropriate concept of balancedness of Cauchy ¯lter pairs with respect tothat family. In this way we obtain a general theory of the B-completion fora subbasic T0-family of quasi-pseudometrics that can be applied to the studyof any quasi-uniform space.","abstract_has_math":false,"creators":["Kivuvu, Charly Makitu"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Künzi, Hans-Peter A"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:23:21Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/6665","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Künzi, Hans-Peter A"]},{"key":"dc:creator","label":"Author","values":["Kivuvu, Charly Makitu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-08-22T10:33:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-08-22T10:33:43Z"]},{"key":"dc:date.issued","label":"Date","values":["2010"]},{"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/11427/6665"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The notion of a quiet quasi-uniform space was introduced by Doitchinov in1988 when he developed an interesting completion theory for this class ofquasi-uniform spaces. At the same time Doitchinov developed a similar com-pletion theory for a class of T0-balanced quasi-pseudometric spaces.In my Masters thesis I showed that the Doitchinov completion theory forbalanced quasi-pseudometric spaces can be extended to arbitrary T0-quasi-pseudometric spaces. That completion was called the B-completion.The principal aim of this thesis is to investigate whether the Doitchinov com-pletion theory for quiet quasi-uniform space can be extended to arbitraryT0-quasi-uniform spaces. The main result in this thesis is negative and leadsus to conclude that Doitchinov's completion theory for quiet quasi-uniformspaces cannot be fully extended to arbitrary quasi-uniform spaces, becauseinvestigations due to De¶ak indicate that no suitable concept of a quiet Cauchy¯lter pair exists which could replace the quasi-pseudometric concept of a bal-anced Cauchy ¯lter pair in the quasi-uniform setting. Under these circum-stances we therefore suggest that in an arbitrary quasi-uniform space, weshould work with a nonempty subbasic family of quasi-pseudometrics and anappropriate concept of balancedness of Cauchy ¯lter pairs with respect tothat family. In this way we obtain a general theory of the B-completion fora subbasic T0-family of quasi-pseudometrics that can be applied to the studyof any quasi-uniform space."]},{"key":"dc:title","label":"Title","values":["On Doitchinov's quietness for arbitrary quasi-uniform spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Künzi, Hans-Peter A"],"dc:creator":["Kivuvu, Charly Makitu"],"dc:date.accessioned":["2014-08-22T10:33:43Z"],"dc:date.available":["2014-08-22T10:33:43Z"],"dc:date.issued":["2010"],"dc:description.abstract":["The notion of a quiet quasi-uniform space was introduced by Doitchinov in1988 when he developed an interesting completion theory for this class ofquasi-uniform spaces. At the same time Doitchinov developed a similar com-pletion theory for a class of T0-balanced quasi-pseudometric spaces.In my Masters thesis I showed that the Doitchinov completion theory forbalanced quasi-pseudometric spaces can be extended to arbitrary T0-quasi-pseudometric spaces. That completion was called the B-completion.The principal aim of this thesis is to investigate whether the Doitchinov com-pletion theory for quiet quasi-uniform space can be extended to arbitraryT0-quasi-uniform spaces. The main result in this thesis is negative and leadsus to conclude that Doitchinov's completion theory for quiet quasi-uniformspaces cannot be fully extended to arbitrary quasi-uniform spaces, becauseinvestigations due to De¶ak indicate that no suitable concept of a quiet Cauchy¯lter pair exists which could replace the quasi-pseudometric concept of a bal-anced Cauchy ¯lter pair in the quasi-uniform setting. Under these circum-stances we therefore suggest that in an arbitrary quasi-uniform space, weshould work with a nonempty subbasic family of quasi-pseudometrics and anappropriate concept of balancedness of Cauchy ¯lter pairs with respect tothat family. In this way we obtain a general theory of the B-completion fora subbasic T0-family of quasi-pseudometrics that can be applied to the studyof any quasi-uniform space."],"dc:identifier.uri":["http://hdl.handle.net/11427/6665"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["On Doitchinov's quietness for arbitrary quasi-uniform spaces"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:21Z"}