Convergence structures in M-fuzzifying convex spaces

By Bin Pang. Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2020

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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.

Subfields: Management Science and Operations Research

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