Metrization of ordered topological spaces

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dc.contributor.advisorSalbany, Sergio de Ornelasen_ZA
dc.contributor.authorColquhoun, Alanen_ZA
dc.date.accessioned2016-03-14T07:03:48Z
dc.date.available2016-03-14T07:03:48Z
dc.date.issued1974en_ZA
dc.description.abstractIn 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions necessary for metrizability of such spaces. One of the earliest papers concerned with ordered topological spaces is that of Eilenberg. Since then, ordered spaces have been considered by various authors, but few considered the conditions under which such spaces would be metrizable. Bennet gave a characterization of metrizability for a linearly ordered topological space with a σ-point finite base. A linearly ordered topological space is a space for which the interval topology coincides with the original topology for the space. We investigate the metrizability of linearly ordered topological space satisfying certain covering properties, countability conditions on the base, certain conditions on the diagonal and spaces which admit a symmetric. We obtain four characterizations of metrizability for linearly ordered topological space in terms of some of the above notions.en_ZA
dc.identifier.apacitationColquhoun, A. (1974). <i>Metrization of ordered topological spaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17677en_ZA
dc.identifier.chicagocitationColquhoun, Alan. <i>"Metrization of ordered topological spaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1974. http://hdl.handle.net/11427/17677en_ZA
dc.identifier.citationColquhoun, A. 1974. Metrization of ordered topological spaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Colquhoun, Alan AB - In 1969, Lutzer proved that a linearly ordered topological space with a Gδ-diagonal is metrizable. This appears to be the first work in the field of metrization of ordered topological spaces. Very little seems to have been done in this direction. This thesis is a study of the various conditions necessary for metrizability of such spaces. One of the earliest papers concerned with ordered topological spaces is that of Eilenberg. Since then, ordered spaces have been considered by various authors, but few considered the conditions under which such spaces would be metrizable. Bennet gave a characterization of metrizability for a linearly ordered topological space with a σ-point finite base. A linearly ordered topological space is a space for which the interval topology coincides with the original topology for the space. We investigate the metrizability of linearly ordered topological space satisfying certain covering properties, countability conditions on the base, certain conditions on the diagonal and spaces which admit a symmetric. We obtain four characterizations of metrizability for linearly ordered topological space in terms of some of the above notions. DA - 1974 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1974 T1 - Metrization of ordered topological spaces TI - Metrization of ordered topological spaces UR - http://hdl.handle.net/11427/17677 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17677
dc.identifier.vancouvercitationColquhoun A. Metrization of ordered topological spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1974 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17677en_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.otherApplied Mathematicsen_ZA
dc.subject.otherTopologyen_ZA
dc.titleMetrization of ordered topological spacesen_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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