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

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

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