International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 209-216
doi:10.1155/S0161171287000279
Order compatibility for Cauchy spaces and convergence spaces
Darrell C. Kent1
and Reino Vainio2
1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USA
2AA}bo Akademi, Matematiska Institutionen, Fänriksgatan 3, Åbo 50 SF-20500, Finland
Abstract
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.