Fuzzy convergence structures in the framework of L-convex spaces
نویسندگان
1 College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
2 School of Mathematics and Information Sciences, Yantai University, Yantai, China
3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
doi
10.22111/ijfs.2020.5411چکیده
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.
