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Uniformities induced by cozero and Baire sets


Author: Anthony W. Hager
Journal: Proc. Amer. Math. Soc. 63 (1977), 153-159
MSC: Primary 54E15
DOI: https://doi.org/10.1090/S0002-9939-1977-0436082-8
MathSciNet review: 0436082
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Abstract: This paper treats the cozero- and Baire-fine uniform spaces, those X such that each cozero (resp., Baire) function on X is uniformly continuous. The emphasis is on the general method, with the results about coz and Ba as corollaries. Some of these, stated just for coz: The coz functor out of Unif has no left adjoint, but its restrictions to precompact, and to separable, spaces do. A space is coz-fine iff it is proximally fine and each finite coz-cover is uniform. A cozero field $ \mathcal{A}$ has a compatible coz-fine uniform space iff the meet of two completely additive $ \mathcal{A}$ -covers is another.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0436082-8
Keywords: Uniform space, cozero set, cozero function, Baire set, Baire function, proximity, cozero-fine, Baire-fine, proximally-fine, coreflection
Article copyright: © Copyright 1977 American Mathematical Society

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