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Non-Metrizable Uniformities and Proximities on Metrizable Spaces
Published online by Cambridge University Press: 20 November 2018
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In the literature there exist examples of metrizable spaces admitting nonmetrizable uniformities (e.g., see [3, Problem C, p. 204]). In this paper, this phenomenon is presented more coherently by showing that every non-compact metrizable space admits at least one non-metrizable proximity and uncountably many non-metrizable uniformities. It is also proved that the finest compatible uniformity (proximity) on a non-compact non-semidiscrete space is always non-metrizable.
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- Copyright © Canadian Mathematical Society 1973
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