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dc.contributor.advisor Siweya, Hlengani J. Matabane, Mogalatjane Edward 2013-04-15T09:28:15Z 2013-04-15T09:28:15Z 2012
dc.description Thesis (MA. (Mathematics)) -- University of Limpopo, 2012 en_US
dc.description.abstract Topological structures called Yosida frames and related algebraic frames are studied in the realm of Pointfree Topology. It is shown that in algebraic frames regular elements are those for which compact elements are rather below the regular elements, and algebraic frames are regular if and only if every compact element is rather below itself if and only if the frame has the Finite Intersection Property (FIP) and each prime element is minimal. We also show that Yosida frames are those algebraic frames with the Finite Intersection Property and are finitely subfit; that these frames are also those semi-simple algebraic frames with FIP and a disjointification where dim (L)≤ 1; and we prove that in an algebraic frame with FIP, it holds that dom (L) = dim (L). In relation to normality in Yosida frames, we show that in a coherent normal Yosida frame L, the frame is subfit if and only if it is regular if and only if it is zero- dimensional if and only if every compact element is complemented. en_US
dc.format.extent vi, 57 leaves en_US
dc.language.iso en en_US
dc.relation.requires Adobe acrobat reader, version 7 en_US
dc.subject Topological structures en_US
dc.subject Algebraic frames en_US
dc.subject.lcsh Topology en_US
dc.subject.lcsh Algebraic topology en_US
dc.subject.lcsh Ordered algebraic structures en_US
dc.title On yosida frames and related frames en_US
dc.type Thesis en_US

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