Cauchy complete nearness spaces
Every nearness space has a strict complete regular nearness completion. For regular nearness spaces this provides a reflection, but for \(N_2\)-spaces the strict completion may fail to be a reflection. The authors improve this situation by introducing the concepts of Cauchy complete nearness spaces, Cauchy maps and Cauchy completions (as suitable subspaces of the strict completion), and by demonstrating that Cauchy completions provide a reflection in the category of \(N_2\)-spaces and Cauchy maps.
scientific article; zbMATH DE number 1563347