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On convergence theory in fuzzy topological spaces and its applications. (English) Zbl 1081.54007
Summary: 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 Pao-Ming Pu and Ying-Ming Liu [J. Math. Anal. Appl. 76, 571-599 (1980; Zbl 0447.54006)]. 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.
##### MSC:
 54A40 Fuzzy topology 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54C08 Weak and generalized continuity 54H12 Topological lattices, etc. (topological aspects)
##### Keywords:
fuzzy points; $$Q$$-neighborhoods; fuzzy filters; fuzzy nets; limit
Zbl 0447.54006
Full Text:
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