Quasi-uniform completeness in terms of Cauchy nets
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.
scientific article; zbMATH DE number 878085