dc.contributor.advisor Witbooi, P.J. dc.contributor.author Chishwashwa, Nyumbu dc.date.accessioned 2022-03-01T08:00:43Z dc.date.available 2022-03-01T08:00:43Z dc.date.issued 2007 dc.identifier.uri http://hdl.handle.net/11394/8761 dc.description Masters of Science en_US dc.description.abstract The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between the categories of topological spaces, closure spaces and relational structures. We study the 4-point non-Hausdorff model S4 weakly homotopy equivalent to the circle s'. We study pairings of some objects in the category of relational structures, similar to the multiplication of Hopf spaces in topology. The multiplication S4 x S4 ---7 S4 fails to be order preserving for posets. Nevertheless, applying a single barycentric subdivision on S4 to get Ss, an 8-point model of the circle enables us to define an order preserving poset map Ss x Ss ---7 S4' Restricted to the axes, this map yields weak homotopy equivalences Ss ---7 S4' Hence it is a pairing. Further, using the non-Hausdorff join Ss ® Ss, we obtain a version of the Hopf map Ss ® Ss ---7 §S4. This model of the Hopf map is in fact a map of non-Hausdorff double mapping cylinders. en_US dc.language.iso en en_US dc.publisher University of the Western Cape en_US dc.subject Category en_US dc.subject Functor en_US dc.subject Homotopy en_US dc.subject Weak homotopy equivalence en_US dc.subject Partially ordered set en_US dc.subject Barycentric subdivision en_US dc.subject Binary reflexive relational structure en_US dc.subject Pairing en_US dc.subject Hopf construction en_US dc.subject Finite model en_US dc.title Pairings of binary reflexive relational structures en_US dc.rights.holder University of the Western Cape en_US
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