Note on a result of E.P. Lane
Fletcher, P., Lindgren, W.F. (1976)
Portugaliae mathematica
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Fletcher, P., Lindgren, W.F. (1976)
Portugaliae mathematica
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Romaguera, Salvador (2000)
Mathematica Pannonica
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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...
P. Fletcher (1971)
Colloquium Mathematicae
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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 . 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 generated by the quasi-uniformity , so that many of his preparatory results become consequences of standard topological facts. In particular,...
P. Fletcher (1971)
Colloquium Mathematicae
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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.
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 is equivalent to quasi-compactness of some operator . 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.