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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

On yosida frames and related frames

Matabane, Mogalatjane Edward January 2012 (has links)
Thesis (MA. (Mathematics)) -- University of Limpopo, 2012 / 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.

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