Document Type: Research Paper
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
School of Mathematics and Information Sciences, Yantai University, Yantai, China
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
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.