Proximity and generalized uniformity
E. Alfsen, O. Njastad (1963)
Fundamenta Mathematicae
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E. Alfsen, O. Njastad (1963)
Fundamenta Mathematicae
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Dowker, C. H.
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Miroslav Hušek (2017)
Commentationes Mathematicae Universitatis Carolinae
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Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added.
W. Kulpa (1972)
Colloquium Mathematicae
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N. C. Manna (1970)
Colloquium Mathematicae
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E. Pap (1976)
Matematički Vesnik
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Vilímovský, J.
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Tomi Alaste (2012)
Studia Mathematica
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We show that the uniform compactification of a uniform space (X,𝓤) can be considered as a space of filters on X. We apply these filters to study the ℒ𝓤𝓒-compactification of a topological group.