Uniformities induced by cozero and Baire sets

Hager, Anthony W.

doi:10.1090/S0002-9939-1977-0436082-8

Uniformities induced by cozero and Baire sets
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Proc. Amer. Math. Soc. 63 (1977), 153-159 Request permission

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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Proximally and measurably fine uniform spaces

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Uniformities induced by proximity, cozero, and Baire sets

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