Construction of quasi-metrics determined by orders

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dc.contributor.advisorKünzi, Hans-Peter Aen_ZA
dc.contributor.authorGaba, Yae O K Ulrichen_ZA
dc.date.accessioned2016-07-26T12:15:29Z
dc.date.available2016-07-26T12:15:29Z
dc.date.issued2016en_ZA
dc.description.abstractThe second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology have been done in order to extend known results of the classical theory. It is the aim of this thesis to dig more into this theory by investigating the existence of quasi-pseudometrics that produce a given partially ordered metric space. We show that whenever one has an ordered metric space, it is often possible to describe both the metric and the order using quasi-pseudometrics. We establish respectively topological and algebraic conditions for the existence of such quasi-pseudometrics.We deduct some specific conditions when the ordered metric space(X; m,≤) is assumed to have some topological properties such as compactness. When a producing quasi-pseudo metric exists, the question of uniqueness is also studied. A characterization of produced spaces is given.en_ZA
dc.identifier.apacitationGaba, Y. O. K. U. (2016). <i>Construction of quasi-metrics determined by orders</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/20769en_ZA
dc.identifier.chicagocitationGaba, Yae O K Ulrich. <i>"Construction of quasi-metrics determined by orders."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2016. http://hdl.handle.net/11427/20769en_ZA
dc.identifier.citationGaba, Y. 2016. Construction of quasi-metrics determined by orders. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Gaba, Yae O K Ulrich AB - The second half of the last century has seen a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology have been done in order to extend known results of the classical theory. It is the aim of this thesis to dig more into this theory by investigating the existence of quasi-pseudometrics that produce a given partially ordered metric space. We show that whenever one has an ordered metric space, it is often possible to describe both the metric and the order using quasi-pseudometrics. We establish respectively topological and algebraic conditions for the existence of such quasi-pseudometrics.We deduct some specific conditions when the ordered metric space(X; m,≤) is assumed to have some topological properties such as compactness. When a producing quasi-pseudo metric exists, the question of uniqueness is also studied. A characterization of produced spaces is given. DA - 2016 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2016 T1 - Construction of quasi-metrics determined by orders TI - Construction of quasi-metrics determined by orders UR - http://hdl.handle.net/11427/20769 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/20769
dc.identifier.vancouvercitationGaba YOKU. Construction of quasi-metrics determined by orders. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2016 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/20769en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleConstruction of quasi-metrics determined by ordersen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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