Convergence structures in M-fuzzifying convex spaces

Abstract

By means of M -fuzzifying convex filters, fuzzy convergence structures in the framework of M -fuzzifying convex spaces are proposed, which are called M -fuzzifying convergence structures. It is shown that there is a Galois correspondence between the category of M -fuzzifying convex spaces and that of M -fuzzifying convergence spaces. In particular, the former can be embedded in the latter as a full and reflective subcategory. Also, it is proved that the category of M -fuzzifying preconvex convergence spaces is isomorphic to that of M -fuzzifying preconvex closure spaces, and the category of M -fuzzifying convex convergence spaces is isomorphic to that of M -fuzzifying hull spaces. Finally, a degree approach to separation properties in M -fuzzifying convergence spaces is proposed. The heredity and productivity of S ₀, S ₁ and S ₂-separated properties are investigated in a degree sense.