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\(HC\)-convergence theory of \(L\)-nets and \(L\)-ideals and some of its applications. (English) Zbl 1053.54505
Summary: In this paper we introduce and study the concepts of \(HC\)-closed sets and \(HC\)-limit (\(HC\)-cluster) points of \(L\)-nets and \(L\)-ideals using the notion of almost \(N\)-compact remote neighbourhoods in \(L\)-topological spaces. Then we introduce and study the concept of \(HL\)-continuous mappings. Several characterizations based on \(HC\)-closed sets and the \(HC\)-convergence theory of \(L\)-nets and \(L\)-ideals are presented for \(HL\)-continuous mappings.
MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54A40 Fuzzy topology
54C08 Weak and generalized continuity
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