Studies on ultraquasi-pseudometrics and orderings

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dc.contributor.advisorKünzi, Hans-Peter Aen_ZA
dc.contributor.authorSolofomananirina Tiantsoa, Francky Mathieuen_ZA
dc.date.accessioned2018-05-25T07:40:01Z
dc.date.available2018-05-25T07:40:01Z
dc.date.issued2018en_ZA
dc.description.abstractUltraquasi-pseudometric spaces even though quite simple in concept, as it is easily obtained by altering the usual triangle inequality property, still yield interesting results. Indeed, a natural question that should arise is how does switching to the strong triangle inequality affect some of the results we already know about quasi-pseudometrics. On some points we get similar results to those of when we have the standard triangle inequality, but the general observation is that dealing with the strong triangle inequality is easier. Of course, there are results that cannot be obtained without the "ultra-property". A fast rundown on those effects is then deemed necessary to begin with. Also, since we cannot go through every single result on quasi-pseudometrics we then need to localize our observations, that is why in the first part we restrained our observations on the results from Gaba and Künzi about splitting metrics. Also, we will see some particular algorithms and connections to the bicompletion, joincompact ultraquasi-metric spaces and the old construction of a total order by Herrlich.en_ZA
dc.identifier.apacitationSolofomananirina Tiantsoa, F. M. (2018). <i>Studies on ultraquasi-pseudometrics and orderings</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/28113en_ZA
dc.identifier.chicagocitationSolofomananirina Tiantsoa, Francky Mathieu. <i>"Studies on ultraquasi-pseudometrics and orderings."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2018. http://hdl.handle.net/11427/28113en_ZA
dc.identifier.citationSolofomananirina Tiantsoa, F. 2018. Studies on ultraquasi-pseudometrics and orderings. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Solofomananirina Tiantsoa, Francky Mathieu AB - Ultraquasi-pseudometric spaces even though quite simple in concept, as it is easily obtained by altering the usual triangle inequality property, still yield interesting results. Indeed, a natural question that should arise is how does switching to the strong triangle inequality affect some of the results we already know about quasi-pseudometrics. On some points we get similar results to those of when we have the standard triangle inequality, but the general observation is that dealing with the strong triangle inequality is easier. Of course, there are results that cannot be obtained without the "ultra-property". A fast rundown on those effects is then deemed necessary to begin with. Also, since we cannot go through every single result on quasi-pseudometrics we then need to localize our observations, that is why in the first part we restrained our observations on the results from Gaba and Künzi about splitting metrics. Also, we will see some particular algorithms and connections to the bicompletion, joincompact ultraquasi-metric spaces and the old construction of a total order by Herrlich. DA - 2018 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2018 T1 - Studies on ultraquasi-pseudometrics and orderings TI - Studies on ultraquasi-pseudometrics and orderings UR - http://hdl.handle.net/11427/28113 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/28113
dc.identifier.vancouvercitationSolofomananirina Tiantsoa FM. Studies on ultraquasi-pseudometrics and orderings. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2018 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/28113en_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.titleStudies on ultraquasi-pseudometrics and orderingsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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