Probablistic convergence spaces and regularity
The usual definition of regularity for convergence spaces can be characterized by a diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t-norm T, and the resulting axiom RT defines T-regularity, which is the primary focus of...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000896 |
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| _version_ | 1832562462435573760 |
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| author | P. Brock D. C. Kent |
| author_facet | P. Brock D. C. Kent |
| author_sort | P. Brock |
| collection | DOAJ |
| description | The usual definition of regularity for convergence spaces can be characterized by a
diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t-norm T, and the resulting axiom RT defines T-regularity, which is the primary focus of this paper. We give several characterizations of T-regularity, both in
general and for specific choices of T, and investigate some of its basic properties. |
| format | Article |
| id | doaj-art-3ddf71fbeceb4385a0fb98633b309ef8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3ddf71fbeceb4385a0fb98633b309ef82025-02-03T01:22:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120463764610.1155/S0161171297000896Probablistic convergence spaces and regularityP. Brock0D. C. Kent1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USADepartment of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USAThe usual definition of regularity for convergence spaces can be characterized by a diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t-norm T, and the resulting axiom RT defines T-regularity, which is the primary focus of this paper. We give several characterizations of T-regularity, both in general and for specific choices of T, and investigate some of its basic properties.http://dx.doi.org/10.1155/S0161171297000896convergence spaceprobabilistic convergence spacet-normT-regular spaceT-approachable spacecategory. |
| spellingShingle | P. Brock D. C. Kent Probablistic convergence spaces and regularity International Journal of Mathematics and Mathematical Sciences convergence space probabilistic convergence space t-norm T-regular space T-approachable space category. |
| title | Probablistic convergence spaces and regularity |
| title_full | Probablistic convergence spaces and regularity |
| title_fullStr | Probablistic convergence spaces and regularity |
| title_full_unstemmed | Probablistic convergence spaces and regularity |
| title_short | Probablistic convergence spaces and regularity |
| title_sort | probablistic convergence spaces and regularity |
| topic | convergence space probabilistic convergence space t-norm T-regular space T-approachable space category. |
| url | http://dx.doi.org/10.1155/S0161171297000896 |
| work_keys_str_mv | AT pbrock probablisticconvergencespacesandregularity AT dckent probablisticconvergencespacesandregularity |