Geodesic
HC-convergence theory of $L$-nets and $L$-ideals and some of its applications
Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 349-366

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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.
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.
DOI : 10.21136/MB.2003.134000
Classification : 54A20, 54A40, 54C08, 54H12
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 
Nouh, A. A. HC-convergence theory of $L$-nets and $L$-ideals and some of its applications. Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 349-366. doi: 10.21136/MB.2003.134000
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