Strict extensions in pointfree topology

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dc.contributor.advisorSchauerte, Annelieseen_ZA
dc.contributor.advisorKünzi, Hans-Peter Aen_ZA
dc.contributor.authorApfel, Gayle Renayen_ZA
dc.date.accessioned2014-08-20T19:14:49Z
dc.date.available2014-08-20T19:14:49Z
dc.date.issued2013en_ZA
dc.description.abstractExtensions of spaces have been constructed and used since the 19th century, for example, to form the complex sphere from the complex plane by adding a point at in nity. Once topological spaces were invented in the 20th century, completions and compactications became important examples of extensions. Banaschewski wrote that extension problems have a """"philosophical charm"""" in that they seem to ask the question: """"What possibilities in the unknown are determined by the known?"""" Strict extensions were first defined for topological spaces by Stone. The idea was initially translated into the pointfree setting by Hong, and has since been extensively studied. Just recently, interest has been shown in studying strict extensions in the asymmetric setting of biframes, for example, by Frith and Schauerte. The intention of this dissertation is to provide a systematic and detailed exposition of strict extensions of frames and nearness frames, which can be used as a reference on this topic. For instance, someone interested in pursuing strict extensions of biframes might obtain the relevant background from reading this text, although the topic of strict extensions of biframes itself will not be discussed here.en_ZA
dc.identifier.apacitationApfel, G. R. (2013). <i>Strict extensions in pointfree topology</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/6621en_ZA
dc.identifier.chicagocitationApfel, Gayle Renay. <i>"Strict extensions in pointfree topology."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013. http://hdl.handle.net/11427/6621en_ZA
dc.identifier.citationApfel, G. 2013. Strict extensions in pointfree topology. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Apfel, Gayle Renay AB - Extensions of spaces have been constructed and used since the 19th century, for example, to form the complex sphere from the complex plane by adding a point at in nity. Once topological spaces were invented in the 20th century, completions and compactications became important examples of extensions. Banaschewski wrote that extension problems have a """"philosophical charm"""" in that they seem to ask the question: """"What possibilities in the unknown are determined by the known?"""" Strict extensions were first defined for topological spaces by Stone. The idea was initially translated into the pointfree setting by Hong, and has since been extensively studied. Just recently, interest has been shown in studying strict extensions in the asymmetric setting of biframes, for example, by Frith and Schauerte. The intention of this dissertation is to provide a systematic and detailed exposition of strict extensions of frames and nearness frames, which can be used as a reference on this topic. For instance, someone interested in pursuing strict extensions of biframes might obtain the relevant background from reading this text, although the topic of strict extensions of biframes itself will not be discussed here. DA - 2013 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2013 T1 - Strict extensions in pointfree topology TI - Strict extensions in pointfree topology UR - http://hdl.handle.net/11427/6621 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/6621
dc.identifier.vancouvercitationApfel GR. Strict extensions in pointfree topology. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2013 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/6621en_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.titleStrict extensions in pointfree topologyen_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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