# Article

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Keywords:
$L$-topology; remoted neighbourhood; almost $N$-compactness; $\operatorname{\text{HC}}$-closed set; $\operatorname{\text{HL}}$-continuity; $L$-net; $L$-ideal; $\operatorname{\text{HC}}$-convergence theory
Summary:
In this paper we introduce and study the concepts of $\operatorname{\text{HC}}$-closed set and $\operatorname{\text{HC}}$-limit ($\operatorname{\text{HC}}$-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 $\operatorname{\text{HL}}$-continuous mappings. Several characterizations based on $\operatorname{\text{HC}}$-closed sets and the $\operatorname{\text{HC}}$-convergence theory of $L$-nets and $L$-ideals are presented for $\operatorname{\text{HL}}$-continuous mappings.
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