Functorial uniformization of topological spaces (Q1099837)

Let Unif denote the category of uniform spaces and uniformly continuous maps and Creg the category of completely regular topological spaces and continuous maps. Let T be the forgetful functor from Unif to Creg. The authors study functors that equip spaces in Creg with compatible uniformities, i.e. functors F: Creg\(\to Unif\) with \(TF=1\), so-called T- sections. They develop as a tool the notion of spanning a T-section by a class of uniform spaces, and the order-dual notion of cospanning. Coarsest and finest uniform bireflectors and coreflectors associated with a T-section are characterized. Certain effects of the uniform completion reflector on a T-section are expressed in terms of the associated bireflectors. Clearly the investigations of the authors are motivated by the interesting results that they have obtained in their paper ``Completion-true functorial uniformities''. (A preprint of this paper has appeared in Seminarberichte Fachbereich Math. Informatik, FernUniv. Hagen 19, 95-104 (1984).)