International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 483-496
doi:10.1155/S0161171285000539
Ordered Cauchy spaces
Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USA
Received 1 May 1985
Copyright © 1985 D. C. Kent and R. 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.
Abstract
This paper is concerned with the notion of “ordered Cauchy space” which is given a simple internal characterization in Section 2. It gives a discription of the category of ordered Cauchy spaces which have ordered completions, and a construction of the “fine completion functor” on this category. Sections 4 through 6 deals with certain classes of ordered Cauchy spaces which have ordered completions; examples are given which show that the fine completion does not preserve such properties as uniformizability, regularity, or total boundedness. From these results, it is evident that a further study of ordered Cauchy completions is needed.