Order compatibility for Cauchy spaces and convergence spaces - D. C. Kent; Reino Vainio (International Journal of Mathematics and Mathematical Sciences)
A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi-uniform convergence structure on X. Howover, there are two natural ways to derive the former structures from the latter, leading to strong and weak notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence spaces.