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MATHEMATICA BOHEMICA, Vol. 128, No. 4, pp. 349-366 (2003)
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$ HC$-convergence theory of $L$-nets and $L$-ideals and some of its applications

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A. A. Nouh

* A. A. Nouh*, Mathematics Department, Faculty of Science, Mansoura University, Egypt, e-mail: ` aanouh@hotmail.com`

**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

**Full text of the article:**

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