International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 209-216

Order compatibility for Cauchy spaces and convergence spaces

D. C. Kent1 and Reino Vainio2

1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USA
2Åbo Akademi, Matematiska Institutionen, Fänriksgatan 3, Åbo 50 SF-20500, Finland

Received 28 July 1986

Copyright © 1987 D. C. Kent and Reino Vainio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.