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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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