$M$-fuzzifying convexity-preserving mappings and $M$-fuzzifying closure-preserving mappings

Year 2025, Volume: 54 Issue: 4, 1356 - 1370, 29.08.2025

Fei Li , Manyu Cui

https://doi.org/10.15672/hujms.1574594

Abstract

In this paper, $M$-fuzzifying convexity-preserving mappings between $M$-fuzzifying convergence spaces, and $M$-fuzzifying closure-preserving mappings between $M$-fuzzifying preconvex closure spaces are proposed. The relationships of $M$-fuzzifying convexity-preserving mappings with $M$-CP mappings, $M$-fuzzifying preconvex closure operators, and separation properties in $M$-fuzzifying convergence spaces are discussed. Moreover, it is proved that $S_0$, $S_1$ and $S_2$ separation properties are preserved by homeomorphisms in $M$-fuzzifying convergence spaces.

Keywords

M-fuzzifying convergence space , M-fuzzifying convexity-preserving mapping , M-fuzzifying preconvex closure space , M-fuzzifying closure-preserving mapping , separation axioms

Ethical Statement

This study does not involve human or animal experimentation, and the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supporting Institution

This research was funded by the National Natural Science Foundation of China (Nos.12371462) and the Fundamental Research Funds for the Central Universities (No.2019zy20).

Project Number

Nos.12371462；No.2019zy20

Thanks

We would like to thank the referees and the editor for their constructive suggestions.

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