Convergence structures in M-fuzzifying convex spaces

Abstract

By means of M-fuzzifying convex lters, 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 S₀, S₁ and S₂-separated properties are investigated in a degree sense.

Mathematics Subject Classification (2010): 54A40, 54A20, 52A01.