Ordered Cauchy spaces

D. C. Kent and R. Vainio

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-14

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.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:514379

DOI: 10.1155/S0161171285000539

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