Displaying similar documents to “Entourage Uniformities for Frames.”

Weil uniformities for frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

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In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is...

Totally bounded frame quasi-uniformities

Peter Fletcher, Worthen N. Hunsaker, William F. Lindgren (1993)

Commentationes Mathematicae Universitatis Carolinae

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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...

Quasi-uniform Space

Roland Coghetto (2016)

Formalized Mathematics

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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.