Syntopogenous structures and real-compactness

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dc.contributor.advisorBrümmer, Guillaume C Len_ZA
dc.contributor.authorFlax, Cyril Leeen_ZA
dc.date.accessioned2016-03-30T07:08:28Z
dc.date.available2016-03-30T07:08:28Z
dc.date.issued1972en_ZA
dc.description.abstractThe syntopogenous structures were introduced by Á. Császár. These are generalisations of classical continuity structures such as topologies, proximities and uniformities. In his book, Foundations of General Topology (1963) (Preceded by a French (1960) and a German (1963) edition), Császár treated many properties of syntopgenous structures. Among these properties were completeness and compactness, but not realcompactness. Our purpose was to extend the definition of realcompactness from uniformisable topologies to arbitrary syntopogenous structures and to produce a real compact reflection for arbitrary syntopogenous structures. We did not fully accomplish this purpose. We have, in fact, first defined a notion of quasirealcompactness for arbitrary syntopogenous structures. For uniformisable Hausdorff topologies, realcompactness implies quasirealcompactness; we could not prove or disprove the converse implication. Nevertheless, we were able to give a characterisation of realcompactness for a uniformisable Hausdorff topology in terms of quasirealcompactness of a certain induced proximity; moreover, we produced a double quasirealcompact reflection in the category of separated syntopogenous structures, and from this retrieved the classical Hewitt realcompact reflection.en_ZA
dc.identifier.apacitationFlax, C. L. (1972). <i>Syntopogenous structures and real-compactness</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18367en_ZA
dc.identifier.chicagocitationFlax, Cyril Lee. <i>"Syntopogenous structures and real-compactness."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1972. http://hdl.handle.net/11427/18367en_ZA
dc.identifier.citationFlax, C. 1972. Syntopogenous structures and real-compactness. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Flax, Cyril Lee AB - The syntopogenous structures were introduced by Á. Császár. These are generalisations of classical continuity structures such as topologies, proximities and uniformities. In his book, Foundations of General Topology (1963) (Preceded by a French (1960) and a German (1963) edition), Császár treated many properties of syntopgenous structures. Among these properties were completeness and compactness, but not realcompactness. Our purpose was to extend the definition of realcompactness from uniformisable topologies to arbitrary syntopogenous structures and to produce a real compact reflection for arbitrary syntopogenous structures. We did not fully accomplish this purpose. We have, in fact, first defined a notion of quasirealcompactness for arbitrary syntopogenous structures. For uniformisable Hausdorff topologies, realcompactness implies quasirealcompactness; we could not prove or disprove the converse implication. Nevertheless, we were able to give a characterisation of realcompactness for a uniformisable Hausdorff topology in terms of quasirealcompactness of a certain induced proximity; moreover, we produced a double quasirealcompact reflection in the category of separated syntopogenous structures, and from this retrieved the classical Hewitt realcompact reflection. DA - 1972 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1972 T1 - Syntopogenous structures and real-compactness TI - Syntopogenous structures and real-compactness UR - http://hdl.handle.net/11427/18367 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/18367
dc.identifier.vancouvercitationFlax CL. Syntopogenous structures and real-compactness. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1972 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18367en_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.subject.otherTopologyen_ZA
dc.titleSyntopogenous structures and real-compactnessen_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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