Functorial uniformization of topological spaces
type: Item
instance of: scholarly article
title: Functorial uniformization of topological spaces
zbMATH Open document ID: 0639.54019
DOI: 10.1016/0166-8641(87)90099-X
author: G. C. L. Brümmer
author: Anthony W. Hager
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: 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).)
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 4042815
zbMATH Keywords: category of uniform spaces
zbMATH Keywords: category of completely regular topological spaces
zbMATH Keywords: spanning
zbMATH Keywords: bireflectors and coreflectors
zbMATH Keywords: uniform completion reflector
zbMATH Keywords: T-section
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042815