Characterization of convergence in fuzzy topological spaces
In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule lim which to any prefilter 𝔇 on X assigns, a function lim𝔇∈[0,1]X. We giv...
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| Main Authors: | , |
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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 |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000540 |
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| _version_ | 1832547416986877952 |
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| author | E. Lowen R. Lowen |
| author_facet | E. Lowen R. Lowen |
| author_sort | E. Lowen |
| collection | DOAJ |
| description | In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule lim which to any prefilter 𝔇 on X assigns, a function lim𝔇∈[0,1]X. We give necessary and sufficient conditions for the function 𝔇→lim𝔇 in order that it can be derived from a fuzzy topology. |
| format | Article |
| id | doaj-art-27c36c6596214fe381912e91456e047e |
| 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-27c36c6596214fe381912e91456e047e2025-02-03T06:44:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018349751110.1155/S0161171285000540Characterization of convergence in fuzzy topological spacesE. Lowen0R. Lowen1Department of Mathematics, Free University of Brussels, Brussels 1050, BelgiumDienst Wiskundige Analyse, University of Antwerp, R.U.C.A. 2020, Antwerp, BelgiumIn a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule lim which to any prefilter 𝔇 on X assigns, a function lim𝔇∈[0,1]X. We give necessary and sufficient conditions for the function 𝔇→lim𝔇 in order that it can be derived from a fuzzy topology.http://dx.doi.org/10.1155/S0161171285000540fuzzy topologyprefilterconvergencediagonal operator. |
| spellingShingle | E. Lowen R. Lowen Characterization of convergence in fuzzy topological spaces International Journal of Mathematics and Mathematical Sciences fuzzy topology prefilter convergence diagonal operator. |
| title | Characterization of convergence in fuzzy topological spaces |
| title_full | Characterization of convergence in fuzzy topological spaces |
| title_fullStr | Characterization of convergence in fuzzy topological spaces |
| title_full_unstemmed | Characterization of convergence in fuzzy topological spaces |
| title_short | Characterization of convergence in fuzzy topological spaces |
| title_sort | characterization of convergence in fuzzy topological spaces |
| topic | fuzzy topology prefilter convergence diagonal operator. |
| url | http://dx.doi.org/10.1155/S0161171285000540 |
| work_keys_str_mv | AT elowen characterizationofconvergenceinfuzzytopologicalspaces AT rlowen characterizationofconvergenceinfuzzytopologicalspaces |