On quasi-uniform space valued semi-continuous functions

Tomasz Kubiak; María Angeles de Prada Vicente

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This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity $◃$ on a frame $L$ there is a totally bounded quasi-uniformity on $L$ that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines $◃$ . The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum $ψ L$ and the compactification $ℜ L$ of a uniform frame $(L, 𝐔)$ are meaningful for quasi-uniform frames. If $𝐔$ is a totally bounded...

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Quasi-uniform Space

Roland Coghetto (2016)

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In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space. We define the topology induced by a quasi-uniform space. Finally we formalize from the sets of the form ((X Ω) × X) ∪ (X × Ω), the Csaszar-Pervin quasi-uniform space induced by a topological space.