Uniformities induced by cozero and Baire sets

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 A \mathcal {A} has a compatible coz-fine uniform space iff the meet of two completely additive A \mathcal {A} -covers is another.