Fuzzy convergence structures in the framework of l-convex spaces

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.