Functorial uniformization of topological spaces
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).)
category of completely regular topological spaces
scientific article; zbMATH DE number 4042815
scientific article