Order compatibility for Cauchy spaces and convergence spaces
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000279 |
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| _version_ | 1832545670731399168 |
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| author | D. C. Kent Reino Vainio |
| author_facet | D. C. Kent Reino Vainio |
| author_sort | D. C. Kent |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c04652b1704e497c88a7193760645186 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c04652b1704e497c88a71937606451862025-02-03T07:25:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110220921610.1155/S0161171287000279Order compatibility for Cauchy spaces and convergence spacesD. C. Kent0Reino Vainio1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USAÅbo Akademi, Matematiska Institutionen, Fänriksgatan 3, Åbo 50 SF-20500, FinlandA 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.http://dx.doi.org/10.1155/S0161171287000279preordered Cauchy spacepreordered convergence spaceweakly preordered spacequasi-uniform convergence space. |
| spellingShingle | D. C. Kent Reino Vainio Order compatibility for Cauchy spaces and convergence spaces International Journal of Mathematics and Mathematical Sciences preordered Cauchy space preordered convergence space weakly preordered space quasi-uniform convergence space. |
| title | Order compatibility for Cauchy spaces and convergence spaces |
| title_full | Order compatibility for Cauchy spaces and convergence spaces |
| title_fullStr | Order compatibility for Cauchy spaces and convergence spaces |
| title_full_unstemmed | Order compatibility for Cauchy spaces and convergence spaces |
| title_short | Order compatibility for Cauchy spaces and convergence spaces |
| title_sort | order compatibility for cauchy spaces and convergence spaces |
| topic | preordered Cauchy space preordered convergence space weakly preordered space quasi-uniform convergence space. |
| url | http://dx.doi.org/10.1155/S0161171287000279 |
| work_keys_str_mv | AT dckent ordercompatibilityforcauchyspacesandconvergencespaces AT reinovainio ordercompatibilityforcauchyspacesandconvergencespaces |