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Monadic properties of uniformities


Authors: D. G. Coyle and M. E. Szabo
Journal: Proc. Amer. Math. Soc. 89 (1983), 346-350
MSC: Primary 54J05; Secondary 03H05, 54E15, 54E25
DOI: https://doi.org/10.1090/S0002-9939-1983-0712649-7
MathSciNet review: 712649
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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce the nonstandard concept of a monadic set and characterize diagonal and covering uniformities in terms of such sets. This formulation relates the two fundamental aspects of uniformities directly and obviates the need for bases. We illustrate the utility of our approach by showing that it leads to significant simplifications of the standard proofs characterizing pseudo-metrizable uniform and uniformizable topological spaces.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0712649-7
Keywords: Monadic sets, uniformities, pseudo-metrics, nonstandard, pseudo-metrizable, uniformizable, topological
Article copyright: © Copyright 1983 American Mathematical Society