<i>HB</i>-Continuous Mappings in <i>L</i>-Topological Space

Abstract

In this paper, we introduce and study the notion of <i>HB</i>-closed sets in <i>L</i>-topological space. Then, <i>HB</i>-convergence theory for <i>L</i>-molecular nets and <i>L</i>-ideals is established in terms of <i>HB</i>-closedness. Finally, we give a new definition of fuzzy <i>H</i>-continuous <a href="#ref1">[1]</a> which is called <i>HB</i>-continuity on the basis of the notion of <i>H</i>-bounded <i>L</i>-subsets in <i>L</i>-topological space. Then we give characterizations and properties by making use of <i>HB</i>-converges theory of <i>L</i>-molecular nets and <i>L</i>-ideals.