Ordered Cauchy spaces
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...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000539 |
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| _version_ | 1832555529323413504 |
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| author | D. C. Kent R. Vainio |
| author_facet | D. C. Kent R. Vainio |
| author_sort | D. C. Kent |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4c82a6dc49134f288ed15aea56ebde9e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4c82a6dc49134f288ed15aea56ebde9e2025-02-03T05:47:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018348349610.1155/S0161171285000539Ordered Cauchy spacesD. C. Kent0R. Vainio1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USADepartment of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USAThis 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.http://dx.doi.org/10.1155/S0161171285000539ordered Cauchy spacesordered completionsuniformizabilityregularitytotal boundedness. |
| spellingShingle | D. C. Kent R. Vainio Ordered Cauchy spaces International Journal of Mathematics and Mathematical Sciences ordered Cauchy spaces ordered completions uniformizability regularity total boundedness. |
| title | Ordered Cauchy spaces |
| title_full | Ordered Cauchy spaces |
| title_fullStr | Ordered Cauchy spaces |
| title_full_unstemmed | Ordered Cauchy spaces |
| title_short | Ordered Cauchy spaces |
| title_sort | ordered cauchy spaces |
| topic | ordered Cauchy spaces ordered completions uniformizability regularity total boundedness. |
| url | http://dx.doi.org/10.1155/S0161171285000539 |
| work_keys_str_mv | AT dckent orderedcauchyspaces AT rvainio orderedcauchyspaces |