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Abstract
Considering a completely distributive lattice L as the lattice background, the concepts of L-ordered N-convergence structures and L-fuzzy N-convergence structures are introduced. It is shown that the categories of these two kinds of fuzzy convergence spaces can contain that of L-fuzzy topological spaces as a reflective subcategory. Moreover, it is proved that the categories of topological L-ordered N-convergence spaces, topological L-fuzzy N-convergence spaces and L-fuzzy topological spaces are isomorphic.
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In this paper, fuzzy convergence theory in the framework of L-convex spaces is introduced. Firstly, the concept of L-convex remote-neighborhood spaces is introduced and it is shown that the resulting category is isomorphic to that of L-convex spaces. Secondly, by means of L-convex ideals, the notion of L-convergence spaces is introduced and it is proved that the category of L-convex spaces can be embedded in that of L-convergence spaces as a reflective subcategory. Finally, the concepts of convex and preconvex L-convergence spaces are introduced and it is shown that the resulting categories are isomorphic to the categories of L-convex spaces and L-preconvex remote-neighborhood spaces, respectively. © 2020, University of Sistan and Baluchestan. All rights reserved.