M-fuzzifying convex quasi-uniform spaces

Article type: Research Article

Authors: Wu, Xiu-Yun^{; *} | Niu, Yu-Jie | Zhang, Hui-Min

Affiliations: School of Mathematics and Statistics, Anhui Normal University, Wuhu, China

Correspondence: [*] Corresponding author. Xiu-Yun Wu, School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241003, China. E-mail: [email protected].

Abstract: In this paper, the notion of M-fuzzifying convex remotehood systems is introduced and characterizations of M-fuzzifying convex spaces are obtained. Further, notions of remote mappings and M-fuzzifying convex quasi-uniformities are introduced. It is proved that M-fuzzifying convex quasi-uniform space and M-fuzzifying convex space are mutually induced. In order to discuss categorical relationships among M-fuzzifying convex quasi-uniform spaces, M-fuzzifying convex remotehood spaces and M-fuzzifying convex spaces, notions of M-fuzzifying quasi-uniformizable convex structures and M-fuzzifying quasi-uniformizable convex remotehood spaces are presented. It is proved that the category of M-fuzzifying quasi-uniformizable convex spaces and the category of M-fuzzifying quasi-uniformizable convex remotehood spaces can be embedded into the category of M-fuzzifying convex quasi-uniform spaces as subcategories.

Keywords: M-fuzzifying convex space, M-fuzzifying convex remotehood space, M-fuzzifying quasi-uniformizable convex space, M-fuzzifying convex quasi-uniform space, M-fuzzifying quasi-uniform preserving mapping

DOI: 10.3233/JIFS-223036

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 3, pp. 4371-4382, 2023