Convergence structures in M-fuzzifying convex spaces. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Pang, Bin
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 11(2020)
• Page Start: 1541
• Page End: 1561
• Publication Date: 2020-11-01
• Subjects: 54A40 -- 54A20 -- 52A01; Fuzzy convergence -- fuzzy convex structure -- separation axiom; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1637379
• Languages: English
• ISSNs: 1607-3606

Abstract

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.