$ HC$-convergence theory of $L$-nets and $L$-ideals and some of its applications

Abstract: In this paper we introduce and study the concepts of $\HC$-closed set and $\HC$-limit ($\HC$-cluster) points of $L$-nets and $L$-ideals using the notion of almost $N$-compact remoted 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.

Keywords: $L$-topology, remoted neighbourhood, almost $N$-compactness, $\HC$-closed set, $\HL$-continuity, $L$-net, $L$-ideal, $\HC$-convergence theory

Classification (MSC2000): 54A20, 54A40, 54C08, 54H123

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