Quasi-uniform completeness in terms of Cauchy nets
type: Item
instance of: scholarly article
title: Quasi-uniform completeness in terms of Cauchy nets
zbMATH Open document ID: 0845.54016
DOI: 10.1007/BF01874606
author: Philipp Sünderhauf
published in: Acta Mathematica Hungarica
publication date: 1996-09-11T00:00:00Z
review text: In previous work cited in this paper, the author and M. B. Smyth have used filters to develop a theory of completion of quasi-uniform spaces within the category TQUS whose objects are the topological quasi-uniform spaces and whose morphisms are the maps that are both continuous and quasi-uniformly continuous. The author now returns to this theory, developing it using nets rather than filters. The use of filters had been entirely satisfactory, and the author's characterization of completeable quasi-uniform spaces as those spaces in which every round Cauchy filter is stable had provided early evidence of the importance of stable filters. Thus the reader who prefers filters to nets might suppose the present approach superfluous. In fact, the paper is a model of mathematical exposition and will interest anyone working with quasi-uniform spaces.
reviewed by: P. Fletcher
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 878085
zbMATH Keywords: nets
zbMATH Keywords: completeable quasi-uniform spaces
MaRDI profile type: Publication
cites work: Q5522002
cites work: Q4892299
cites work: Q3966761
cites work: Bitopological Spaces
cites work: Left K‐Completeness in Quasi‐Metric Spaces
cites work: Q3359391
cites work: Completeness of Quasi-Uniform and Syntopological Spaces
cites work: Q4288289
description: scientific article; zbMATH DE number 878085