(Strongly) zero-dimensional ordered spaces

 

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dc.contributor.advisor Brümmer, Guillaume C L en_ZA
dc.contributor.author Nailana, Kwena Rufus en_ZA
dc.date.accessioned 2016-03-01T07:44:11Z
dc.date.available 2016-03-01T07:44:11Z
dc.date.issued 1993 en_ZA
dc.identifier.citation Nailana, K. 1993. (Strongly) zero-dimensional ordered spaces. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/17403
dc.description Includes bibliographical references. en_ZA
dc.description.abstract The relationship between transitive uniform spaces and zero-dimensional topological spaces was first established by Banaschewski [1957], and was later investigated by Levine [1969]. The theory of transitive quasi-uniform spaces is treated in [Fletcher and Lindgren 1972], [Brummer 1984] and [Kiinzi 1990, 1992a, 1992b,1993]; a convenient presentation for our purpose is to be found in [Fletcher and Lindgren 1982]. After Reilly [1972] introduced the notion of zero-dimensionality in bitopological spaces, Birsan [1974] and Halpin [1974] studied the relationship between transitive quasi-uniform spaces and zero-dimensional bitopological spaces. In this thesis we define a notion of zero-dimensionality in ordered topological spaces and examine the relationship between transitive quasi-uniform spaces and zero-dimensional ordered topological spaces. To a large extent, our presentation is influenced by the situation in bitopological spaces (cf. [Halpin 1974] and [Birsan 1974]), and uses the commutative diagrams which occur in [Schauerte 1988] and [Brummer 1977, 1982]. We also study strongly zero-dimensional ordered topological spaces and their relation with functorial quasi-uniformities. In this respect, our results are influenced by those of [Fora 1984], [Banaschewski and Brummer 1990] and [Kiinzi 1990] for strongly zero-dimensional bitopological spaces. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.subject.other Topology en_ZA
dc.title (Strongly) zero-dimensional ordered spaces 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 Nailana, K. R. (1993). <i>(Strongly) zero-dimensional ordered spaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17403 en_ZA
dc.identifier.chicagocitation Nailana, Kwena Rufus. <i>"(Strongly) zero-dimensional ordered spaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993. http://hdl.handle.net/11427/17403 en_ZA
dc.identifier.vancouvercitation Nailana KR. (Strongly) zero-dimensional ordered spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17403 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Nailana, Kwena Rufus AB - The relationship between transitive uniform spaces and zero-dimensional topological spaces was first established by Banaschewski [1957], and was later investigated by Levine [1969]. The theory of transitive quasi-uniform spaces is treated in [Fletcher and Lindgren 1972], [Brummer 1984] and [Kiinzi 1990, 1992a, 1992b,1993]; a convenient presentation for our purpose is to be found in [Fletcher and Lindgren 1982]. After Reilly [1972] introduced the notion of zero-dimensionality in bitopological spaces, Birsan [1974] and Halpin [1974] studied the relationship between transitive quasi-uniform spaces and zero-dimensional bitopological spaces. In this thesis we define a notion of zero-dimensionality in ordered topological spaces and examine the relationship between transitive quasi-uniform spaces and zero-dimensional ordered topological spaces. To a large extent, our presentation is influenced by the situation in bitopological spaces (cf. [Halpin 1974] and [Birsan 1974]), and uses the commutative diagrams which occur in [Schauerte 1988] and [Brummer 1977, 1982]. We also study strongly zero-dimensional ordered topological spaces and their relation with functorial quasi-uniformities. In this respect, our results are influenced by those of [Fora 1984], [Banaschewski and Brummer 1990] and [Kiinzi 1990] for strongly zero-dimensional bitopological spaces. DA - 1993 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1993 T1 - (Strongly) zero-dimensional ordered spaces TI - (Strongly) zero-dimensional ordered spaces UR - http://hdl.handle.net/11427/17403 ER - en_ZA


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