Displaying similar documents to “Totally bounded frame quasi-uniformities”

A Note on Totally Bounded Quasi-Uniformities

Fletcher, P., Hunsaker, W. (1998)

Serdica Mathematical Journal

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We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. The proof was obtained about ten years ago, but never published. In the mean-time several stronger results have been obtained by more direct arguments [8, 9, 10]. In particular it follows from Künzi’s [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy...

On quasi-uniform space valued semi-continuous functions

Tomasz Kubiak, María Angeles de Prada Vicente (2009)

Commentationes Mathematicae Universitatis Carolinae

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F. van Gool [Comment. Math. Univ. Carolin. (1992), 505–523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space ( R , 𝒰 ) . This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology T ( 𝒰 ) generated by the quasi-uniformity 𝒰 , so that many of his preparatory results become consequences of standard topological facts. In particular,...

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.

On quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel'yanov (2011)

Studia Mathematica

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The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net ( T λ ) λ is equivalent to quasi-compactness of some operator T λ . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.