{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/19020"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/19020","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The lattice of quasi-uniformities","abstract":"Over the last thirty years much progress has been made in the investigation of the lattice of uniformities on a set X. In particular, Pelant, Reiterman, Rodl and Simon have published several articles concerning anti-atoms and complements in this lattice. The aim of this dissertation is to begin a similar investigation into the lattice of quasi-uniformities θ(X) on a set X. It starts off with a summary of results obtained for the lattice of topologies on X, which, having been studied in great detail in the past, is intended as an example as to what may be achieved with θ(X). An exposit ion of the lattice of uniformities is then given. We conclude by commencing an investigation into the lattice of quasi-uniformities on X . Where possible, results obtained for the lattice of uniformities are generalized to θ(X), and some original results for θ(X) are also presented.","abstract_html":"Over the last thirty years much progress has been made in the investigation of the lattice of uniformities on a set X. In particular, Pelant, Reiterman, Rodl and Simon have published several articles concerning anti-atoms and complements in this lattice. The aim of this dissertation is to begin a similar investigation into the lattice of quasi-uniformities θ(X) on a set X. It starts off with a summary of results obtained for the lattice of topologies on X, which, having been studied in great detail in the past, is intended as an example as to what may be achieved with θ(X). An exposit ion of the lattice of uniformities is then given. We conclude by commencing an investigation into the lattice of quasi-uniformities on X . Where possible, results obtained for the lattice of uniformities are generalized to θ(X), and some original results for θ(X) are also presented.","abstract_has_math":false,"creators":["De Jager, Eliza P"],"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":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:22:38Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/19020","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":["De Jager, Eliza P"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-04-20T14:08:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-20T14:08:28Z"]},{"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":["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/11427/19020"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["Over the last thirty years much progress has been made in the investigation of the lattice of uniformities on a set X. In particular, Pelant, Reiterman, Rodl and Simon have published several articles concerning anti-atoms and complements in this lattice. The aim of this dissertation is to begin a similar investigation into the lattice of quasi-uniformities θ(X) on a set X. It starts off with a summary of results obtained for the lattice of topologies on X, which, having been studied in great detail in the past, is intended as an example as to what may be achieved with θ(X). An exposit ion of the lattice of uniformities is then given. We conclude by commencing an investigation into the lattice of quasi-uniformities on X . Where possible, results obtained for the lattice of uniformities are generalized to θ(X), and some original results for θ(X) are also presented."]},{"key":"dc:title","label":"Title","values":["The lattice of quasi-uniformities"]}]}],"canonical_facts":{"dc:contributor.advisor":["Künzi, Hans-Peter A"],"dc:creator":["De Jager, Eliza P"],"dc:date.accessioned":["2016-04-20T14:08:28Z"],"dc:date.available":["2016-04-20T14:08:28Z"],"dc:date.issued":["2004"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["Over the last thirty years much progress has been made in the investigation of the lattice of uniformities on a set X. In particular, Pelant, Reiterman, Rodl and Simon have published several articles concerning anti-atoms and complements in this lattice. The aim of this dissertation is to begin a similar investigation into the lattice of quasi-uniformities θ(X) on a set X. It starts off with a summary of results obtained for the lattice of topologies on X, which, having been studied in great detail in the past, is intended as an example as to what may be achieved with θ(X). An exposit ion of the lattice of uniformities is then given. We conclude by commencing an investigation into the lattice of quasi-uniformities on X . Where possible, results obtained for the lattice of uniformities are generalized to θ(X), and some original results for θ(X) are also presented."],"dc:identifier.uri":["http://hdl.handle.net/11427/19020"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["The lattice of quasi-uniformities"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:38Z"}