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A note on metric-fine spaces


Author: Zdeněk Frolík
Journal: Proc. Amer. Math. Soc. 46 (1974), 111-119
MSC: Primary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1974-0358704-X
MathSciNet review: 0358704
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Abstract: The coreflection into metric-fine spaces $ X$ is explicitly described, and it is shown that metric-fine proximally fine spaces are just the spaces $ X$ such that $ f:X \to Y$ is uniformly continuous whenever the pre-images under $ f$ of zero sets are zero sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0358704-X
Keywords: Fine, proximally fine, metric-fine and coz-fine uniformities, completely additive, cozero covers, $ \sigma $-uniformly discrete, coreflection, metrically determined functors
Article copyright: © Copyright 1974 American Mathematical Society

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