Separability and metrisability in locally convex spaces

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dc.contributor.advisorWebb, John Hen_ZA
dc.contributor.authorRobertson, Neill Raymond Charlesen_ZA
dc.date.accessioned2016-09-28T18:59:39Z
dc.date.available2016-09-28T18:59:39Z
dc.date.issued1991en_ZA
dc.descriptionBibliography: pages 58-61.en_ZA
dc.description.abstractThis thesis is devoted to a study of the relationship between separability and metrisability in the context of locally convex spaces. The duality between sep- arability and weak*-metrisability does not carry over to non-metrisable locally convex spaces; the best that can be said in this case is that the equicontinuous subsets in the dual of a separable locally convex space are weak*-metrisable. To get around this difficulty, we often prefer to use the idea of separability by seminorm: a locally convex space E is separable by seminorm if and only if the equicontinuous subsets of its dual are weak*-metrisable. On any locally convex space E there is a finest topology Tχ which is coarser than the given topology and which makes E separable by seminorm. A question that arises is under what conditions a space E is Tχ-complete. In trying to answer this question, we are led to an intriguing binary relation which G.A. Edgar originally defined on the class of Banach spaces. In the first two Chapters of this thesis, we show that many of the results in Edgar's paper can be expressed in terms of the completeness of a space with respect to various topologies.en_ZA
dc.identifier.apacitationRobertson, N. R. C. (1991). <i>Separability and metrisability in locally convex spaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/21966en_ZA
dc.identifier.chicagocitationRobertson, Neill Raymond Charles. <i>"Separability and metrisability in locally convex spaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1991. http://hdl.handle.net/11427/21966en_ZA
dc.identifier.citationRobertson, N. 1991. Separability and metrisability in locally convex spaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Robertson, Neill Raymond Charles AB - This thesis is devoted to a study of the relationship between separability and metrisability in the context of locally convex spaces. The duality between sep- arability and weak*-metrisability does not carry over to non-metrisable locally convex spaces; the best that can be said in this case is that the equicontinuous subsets in the dual of a separable locally convex space are weak*-metrisable. To get around this difficulty, we often prefer to use the idea of separability by seminorm: a locally convex space E is separable by seminorm if and only if the equicontinuous subsets of its dual are weak*-metrisable. On any locally convex space E there is a finest topology Tχ which is coarser than the given topology and which makes E separable by seminorm. A question that arises is under what conditions a space E is Tχ-complete. In trying to answer this question, we are led to an intriguing binary relation which G.A. Edgar originally defined on the class of Banach spaces. In the first two Chapters of this thesis, we show that many of the results in Edgar's paper can be expressed in terms of the completeness of a space with respect to various topologies. DA - 1991 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1991 T1 - Separability and metrisability in locally convex spaces TI - Separability and metrisability in locally convex spaces UR - http://hdl.handle.net/11427/21966 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/21966
dc.identifier.vancouvercitationRobertson NRC. Separability and metrisability in locally convex spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1991 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/21966en_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.titleSeparability and metrisability in locally convex spacesen_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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