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Contributions to the theory of nearness in pointfree topology

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dc.contributor.advisor Dube, T.A. (Prof.) Mugochi, Martin Mandirevesa 2009-12-03T13:45:09Z 2009-12-03T13:45:09Z 2009-09
dc.identifier.citation Mugochi, Martin Mandirevesa (2009) Contributions to the theory of nearness in pointfree topology, University of South Africa, Pretoria, <> en
dc.description.abstract We investigate quotient-fine nearness frames, showing that they are reflective in the category of strong nearness frames, and that, in those with spatial completion, any near subset is contained in a near grill. We construct two categories, each of which is shown to be equivalent to that of quotient-fine nearness frames. We also consider some subcategories of the category of nearness frames, which are co-hereditary and closed under coproducts. We give due attention to relations between these subcategories. We introduce totally strong nearness frames, whose category we show to be closed under completions. We investigate N-homomorphisms and remote points in the context of totally bounded uniform frames, showing the role played by these uniform N-homomorphisms in the transfer of remote points, and their relationship with C -quotient maps. A further study on grills enables us to establish, among other things, that grills are precisely unions of prime filters. We conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a pseudo-frame, by which we mean a poset pretty much like a frame except for the possible absence of the bottom element. en
dc.format.extent 1 online resource (vi, 113 p.)
dc.language.iso en en
dc.subject.ddc 514.2
dc.subject.lcsh Algebraic topology
dc.subject.lcsh Homotopy theory
dc.subject.lcsh Homomorphisms (Mathematics)
dc.title Contributions to the theory of nearness in pointfree topology en
dc.type Thesis en
dc.description.department Mathematical Sciences Ph.D. (Mathematics)

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