FILOMAT

Lin, Shuang

• Vol 39, No 3 (2025) - Ljubisa Kocinac - Topology
  This paper mainly discuss eight kinds of equivalent characterizations of an $M$-fuzzifying topological closure operator $cl:2^{X} \rightarrow M^{X}$, an $M$-fuzzifying topological interior operator $int:2^{X} \rightarrow M^{X}$, and an $M$-fuzzifying topological derived operator $der:2^{X} \rightarrow M^{X}$, in which $M$ is a completely distributive De Morgan algebra. As its applications, we give the fuzzy constructions of $M$-fuzzifying topological operators $cl^{d}$, $int^{d}$, $der^{d}$ induced by an $M$-fuzzifying pseudo metric $d$ in the sense of Morsi's fuzzy metric and prove that the continuity between $M$-fuzzifying topological operator spaces and $M$-fuzzifying pseudo metric spaces is maintained. Finally, we show that the $M$-fuzzifying topological ${\mathcal{T}}$ induced by $d$ is exactly the $M$-fuzzifying topological induced by $cl^{d}$, $int^{d}$ and $der^{d}$. Namely, $\mathcal{T}^{d}={\mathcal{T}^{cl}}^{d}={\mathcal{T}^{int}}^{d}={\mathcal{T}^{der}}^{d}$.
  Abstract