Aspects of compactness in convex spaces

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dc.contributor.advisorWebb, J Hen_ZA
dc.contributor.authorCamilleri, Joyceen_ZA
dc.date.accessioned2015-09-14T07:05:49Z
dc.date.available2015-09-14T07:05:49Z
dc.date.issued1969en_ZA
dc.descriptionIncludes bibliography.en_ZA
dc.description.abstractThis thesis has its origin in a ten minute paper presented at the British Mathematical Colloquium in London in 1966. At this reading, a certain class of spaces was introduced by Mr. D. H. Fremlin, who furthermore, cited interesting compactness properties pertaining to these spaces. This work shall be concerned, foremostly, with the provision of proofs for the statements made by Mr. D. H. Fremlin in 1966, and with demonstrations of how these purely topological results have applications to linear topological spaces, with the emphasis placed on those which are locally convex. Our investigations of the 'Fremlin' spaces, and the search for known spaces which satisfy the 'Fremlin' conditions has led to a concentration on the separable and Frechet spaces. These are discussed in chapter 11. On reading this thesis, it will become apparent that an underlying theme is that of weak compactness. We have therefore taken the liberty, of concluding with a chapter which gives various characterisations of this. Each chapter will introduce its own subject matter. New results and different proofs of existing theorems have been obtained.en_ZA
dc.identifier.apacitationCamilleri, J. (1969). <i>Aspects of compactness in convex spaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/13840en_ZA
dc.identifier.chicagocitationCamilleri, Joyce. <i>"Aspects of compactness in convex spaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969. http://hdl.handle.net/11427/13840en_ZA
dc.identifier.citationCamilleri, J. 1969. Aspects of compactness in convex spaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Camilleri, Joyce AB - This thesis has its origin in a ten minute paper presented at the British Mathematical Colloquium in London in 1966. At this reading, a certain class of spaces was introduced by Mr. D. H. Fremlin, who furthermore, cited interesting compactness properties pertaining to these spaces. This work shall be concerned, foremostly, with the provision of proofs for the statements made by Mr. D. H. Fremlin in 1966, and with demonstrations of how these purely topological results have applications to linear topological spaces, with the emphasis placed on those which are locally convex. Our investigations of the 'Fremlin' spaces, and the search for known spaces which satisfy the 'Fremlin' conditions has led to a concentration on the separable and Frechet spaces. These are discussed in chapter 11. On reading this thesis, it will become apparent that an underlying theme is that of weak compactness. We have therefore taken the liberty, of concluding with a chapter which gives various characterisations of this. Each chapter will introduce its own subject matter. New results and different proofs of existing theorems have been obtained. DA - 1969 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1969 T1 - Aspects of compactness in convex spaces TI - Aspects of compactness in convex spaces UR - http://hdl.handle.net/11427/13840 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/13840
dc.identifier.vancouvercitationCamilleri J. Aspects of compactness in convex spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/13840en_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.titleAspects of compactness in convex 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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