International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 483-496
doi:10.1155/S0161171285000539

Ordered Cauchy spaces

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.