Geodesic
On convergence theory in fuzzy topological spaces and its applications
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 295-316
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In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the $Q$-relation and the $Q$-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong $Q$-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the $Q$-relation and the $Q$-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong $Q$-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.
Classification : 54A20, 54A40, 54C08, 54H12
Keywords: fuzzy points; $Q$-neighborhoods; fuzzy filters; fuzzy nets; limit; adherent and $Q$-adherent points of fuzzy filters and fuzzy nets; fuzzy continuity; strong $Q$-compactness 
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Nouh, Ali Ahmed. On convergence theory in fuzzy topological spaces and its applications. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 295-316. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a2/

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