{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/38591"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/38591","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A contribution to the foundations of the theory of Quasifibration","abstract":"The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations.","abstract_html":"The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations.","abstract_has_math":false,"creators":["Witbooi, Peter Joseph"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hardie, K. A."],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995","date_published":"1995","updated_at":"2026-07-22T22:23:16Z","subjects":["mathematics and applied mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/38591","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hardie, K. 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May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations."]},{"key":"dc:title","label":"Title","values":["A contribution to the foundations of the theory of Quasifibration"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hardie, K. A."],"dc:creator":["Witbooi, Peter Joseph"],"dc:date.accessioned":["2023-09-13T13:24:08Z"],"dc:date.available":["2023-09-13T13:24:08Z"],"dc:date.issued":["1995"],"dc:description.abstract":["The concept of quasifibration was invented by Dold and Thom (DT]. May (M2] approached quasifibrations from a new angle, making use of n-equivalences. This dissertation presents a study of the notion of n-equivalences and related types of maps. The first of our two main goals is to prove a result, Theorem 5.1, which generalizes the fundamental theorem (DT; Satz 2.2] by Dold and Thom on globalization of quasifibrations. Secondly we show that by means of adjunction or clutching constructions, this theorem enables us to retrieve the famous results of James (J2; Theorem 1.2 and Theorem 1.3] in his work on suspension of spheres. The results of James appear in the thesis as Theorem 13.8. For some of the applications we need a generalized version of n-equivalence. This generalization entails replacing, in the definition of n-equivalence, the isomorphisms by isomorphisms modulo a suitable Serre class [Se] of abelian groups. For the sake of having the thesis self-contained, we include a formal discussion of localization of 1-connected spaces and Serre classes of abelian groups. This summarizes the scope of the thesis. More detail on the content of the thesis will be given after we have sketched a historical perspective on quasifibrations."],"dc:identifier.uri":["http://hdl.handle.net/11427/38591"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["mathematics and applied mathematics"],"dc:title":["A contribution to the foundations of the theory of Quasifibration"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral","PhD"]},"updated_at":"2026-07-22T22:23:16Z"}