{"id":{"repo_id":"nwu-za","oai_identifier":"oai:repository.nwu.ac.za:10394/35218"},"canonical_url":"https://search.dev.ndltd.org/etd/nwu-za/oai:repository.nwu.ac.za:10394/35218","repository":{"repo_id":"nwu-za","name":"North-West University (South Africa)","base_url":"https://repository.nwu.ac.za/server/oai/request"},"display":{"title":"On Modular Quasi-Pseudometric Spaces","abstract":"In this MSc dissertation, we present modular metric spaces in asymmetric settings (called modular quasi-pseudometric spaces). Our results generalise and extend the concept of a modular metric on an arbitrary set, as presented in the work of Chistyakov. We show that Chistyakov's results also hold in an asymmetric framework. Furthermore, we show that most of Chistyakov's results do not need the symmetry property of a modular metric and prove that the results even hold when the symmetric property is not assumed. Finally, we observe that for any modular quasipseudometric which is convex on a set, its conjugate modular quasi-pseudometric is also convex and its symmetrized modular pseudometric preserves convexity.","abstract_html":"In this MSc dissertation, we present modular metric spaces in asymmetric settings (called modular quasi-pseudometric spaces). Our results generalise and extend the concept of a modular metric on an arbitrary set, as presented in the work of Chistyakov. We show that Chistyakov's results also hold in an asymmetric framework. Furthermore, we show that most of Chistyakov's results do not need the symmetry property of a modular metric and prove that the results even hold when the symmetric property is not assumed. Finally, we observe that for any modular quasipseudometric which is convex on a set, its conjugate modular quasi-pseudometric is also convex and its symmetrized modular pseudometric preserves convexity.","abstract_has_math":false,"creators":["Sebogodi, K."],"institution":"North-West University (South Africa)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Olela Otafudu, O.","Mushaandja, Z."],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-24T03:33:47Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10394/35218","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Olela Otafudu, O.","Mushaandja, Z."]},{"key":"dc:creator","label":"Author","values":["Sebogodi, K."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-07-20T14:52:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-07-20T14:52:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["North-West University (South Africa)"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10394/35218"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["MSc (Mathematics), North-West University, Mafikeng Campus"]},{"key":"dc:description.abstract","label":"Abstract","values":["In this MSc dissertation, we present modular metric spaces in asymmetric settings (called modular quasi-pseudometric spaces). Our results generalise and extend the concept of a modular metric on an arbitrary set, as presented in the work of Chistyakov. We show that Chistyakov's results also hold in an asymmetric framework. Furthermore, we show that most of Chistyakov's results do not need the symmetry property of a modular metric and prove that the results even hold when the symmetric property is not assumed. Finally, we observe that for any modular quasipseudometric which is convex on a set, its conjugate modular quasi-pseudometric is also convex and its symmetrized modular pseudometric preserves convexity."]},{"key":"dc:title","label":"Title","values":["On Modular Quasi-Pseudometric Spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Olela Otafudu, O.","Mushaandja, Z."],"dc:creator":["Sebogodi, K."],"dc:date.accessioned":["2020-07-20T14:52:26Z"],"dc:date.available":["2020-07-20T14:52:26Z"],"dc:date.issued":["2016"],"dc:description":["MSc (Mathematics), North-West University, Mafikeng Campus"],"dc:description.abstract":["In this MSc dissertation, we present modular metric spaces in asymmetric settings (called modular quasi-pseudometric spaces). Our results generalise and extend the concept of a modular metric on an arbitrary set, as presented in the work of Chistyakov. We show that Chistyakov's results also hold in an asymmetric framework. Furthermore, we show that most of Chistyakov's results do not need the symmetry property of a modular metric and prove that the results even hold when the symmetric property is not assumed. Finally, we observe that for any modular quasipseudometric which is convex on a set, its conjugate modular quasi-pseudometric is also convex and its symmetrized modular pseudometric preserves convexity."],"dc:identifier.uri":["http://hdl.handle.net/10394/35218"],"dc:language.iso":["en"],"dc:publisher":["North-West University (South Africa)"],"dc:title":["On Modular Quasi-Pseudometric Spaces"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T03:33:47Z"}