Stability of barrelled topologies

 

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dc.contributor.advisor Webb, John H en_ZA
dc.contributor.author Burton, Michael Howard en_ZA
dc.date.accessioned 2016-02-12T07:12:40Z
dc.date.available 2016-02-12T07:12:40Z
dc.date.issued 1983 en_ZA
dc.identifier.citation Burton, M. 1983. Stability of barrelled topologies. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/16974
dc.description Bibliography: leaf 86-88. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.title Stability of barrelled topologies en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Burton, 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/11427/16974 en_ZA
dc.identifier.chicagocitation Burton, 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/11427/16974 en_ZA
dc.identifier.vancouvercitation Burton 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/11427/16974 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


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