Stability of barrelled topologies

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dc.contributor.advisorWebb, John Hen_ZA
dc.contributor.authorBurton, Michael Howarden_ZA
dc.date.accessioned2016-02-12T07:12:40Z
dc.date.available2016-02-12T07:12:40Z
dc.date.issued1983en_ZA
dc.descriptionBibliography: leaf 86-88.en_ZA
dc.description.abstractIn the theory of locally convex topological vector spaces, barrelled topologies have been found to be stable under the formation of products, sums and quotients. We shall in this thesis investigate the stability of barrelled topologies with respect to two further mathematical constructions. Firstly, we examine the situation with regard to the formation of finite-codimensional and countable-codimensional subspaces. (Of course, barrelled topologies are not stable under the formation of arbitrary subspaces.) Secondly, we present what is known about the stability of barrelled topologies with respect to enlargements of the dual space - a concept which is defined in the sequel. This aspect of the stability question was tackled in a recent paper by Robertson and Yeomans and was pursued in two subsequent papers by Tweddle and Yeomans and by Robertson, Tweddle and Yeomans. In the next two chapters, we turn our attention to quasibarrelled topologies and we pursue a parallel investigation to that of the first two chapters. Finally we conduct a similar investigation on σ-barrelled and σ-quasibarrelled spaces. The results 5.2, 5.3, 5.4, 5.5, 5.6, 6.2, 6.3, 6.4 and 6.5 concerning these spaces are original.en_ZA
dc.identifier.apacitationBurton, M. H. (1983). <i>Stability of barrelled topologies</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/16974en_ZA
dc.identifier.chicagocitationBurton, Michael Howard. <i>"Stability of barrelled topologies."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1983. http://hdl.handle.net/11427/16974en_ZA
dc.identifier.citationBurton, M. 1983. Stability of barrelled topologies. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Burton, Michael Howard AB - In the theory of locally convex topological vector spaces, barrelled topologies have been found to be stable under the formation of products, sums and quotients. We shall in this thesis investigate the stability of barrelled topologies with respect to two further mathematical constructions. Firstly, we examine the situation with regard to the formation of finite-codimensional and countable-codimensional subspaces. (Of course, barrelled topologies are not stable under the formation of arbitrary subspaces.) Secondly, we present what is known about the stability of barrelled topologies with respect to enlargements of the dual space - a concept which is defined in the sequel. This aspect of the stability question was tackled in a recent paper by Robertson and Yeomans and was pursued in two subsequent papers by Tweddle and Yeomans and by Robertson, Tweddle and Yeomans. In the next two chapters, we turn our attention to quasibarrelled topologies and we pursue a parallel investigation to that of the first two chapters. Finally we conduct a similar investigation on σ-barrelled and σ-quasibarrelled spaces. The results 5.2, 5.3, 5.4, 5.5, 5.6, 6.2, 6.3, 6.4 and 6.5 concerning these spaces are original. DA - 1983 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1983 T1 - Stability of barrelled topologies TI - Stability of barrelled topologies UR - http://hdl.handle.net/11427/16974 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/16974
dc.identifier.vancouvercitationBurton MH. Stability of barrelled topologies. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1983 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16974en_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.otherMathematicsen_ZA
dc.titleStability of barrelled topologiesen_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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