A contribution to the foundations of the theory of Quasifibration
| dc.contributor.advisor | Hardie, K. A. | |
| dc.contributor.author | Witbooi, Peter Joseph | |
| dc.date.accessioned | 2023-09-13T13:24:08Z | |
| dc.date.available | 2023-09-13T13:24:08Z | |
| dc.date.issued | 1995 | |
| dc.date.updated | 2023-09-13T13:06:11Z | |
| 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.apacitation | Witbooi, P. J. (1995). <i>A contribution to the foundations of the theory of Quasifibration</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/38591 | en_ZA |
| dc.identifier.chicagocitation | Witbooi, Peter Joseph. <i>"A contribution to the foundations of the theory of Quasifibration."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1995. http://hdl.handle.net/11427/38591 | en_ZA |
| dc.identifier.citation | Witbooi, P.J. 1995. A contribution to the foundations of the theory of Quasifibration. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/38591 | en_ZA |
| dc.identifier.ris | TY - Doctoral Thesis AU - Witbooi, Peter Joseph AB - 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. DA - 1995 DB - OpenUCT DP - University of Cape Town KW - mathematics and applied mathematics LK - https://open.uct.ac.za PY - 1995 T1 - A contribution to the foundations of the theory of Quasifibration TI - A contribution to the foundations of the theory of Quasifibration UR - http://hdl.handle.net/11427/38591 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/38591 | |
| dc.identifier.vancouvercitation | Witbooi PJ. A contribution to the foundations of the theory of Quasifibration. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1995 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/38591 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| 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 | |
| dc.type.qualificationlevel | PhD |