$\tilde{I}$-proximity spaces based on soft sets
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In this paper, we present a new structure of basic proximity of soft sets based on the notion of soft ideal. For $\tilde{I}=\{\tilde{\Phi}\},$ we have the basic proximity of soft sets and for other types of $\tilde{I}$ we obtain many types of basic proximity structure of soft sets. Also we redefine this structure by using soft ideals. Some results of these spaces are: if $(X,E,\tau )$ is $\tilde{I}$% -soft normal space and $(X,E,\tau ^{\ast })$ is $R_{0}^{^{\prime }}$-space, then there exists $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ such that $\tau ^{\ast }=\tau _{\delta _{\tilde{I}}}$. Also the soft topology generated by $\tilde{I}$-basic proximity of soft sets is finer than the soft topology generated by $R_{0}^{^{\prime }}$-$\check{C}$ech closure operator of soft sets. Finally, for a bijective soft map $% f:(X,E_{1})\rightarrow (Y,E_{2},\delta _{f(\tilde{I})}),$ we construct the largest $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ on $(X,E_{1})$ such that $f$ is $\tilde{I}$-proximally soft continuous mapping.
Abstract
In this paper, we present a new structure of basic proximity of soft sets based on the notion of soft ideal. For $\tilde{I}=\{\tilde{\Phi}\},$ we have the basic proximity of soft sets and for other types of $\tilde{I}$ we obtain many types of basic proximity structure of soft sets. Also we redefine this structure by using soft ideals. Some results of these spaces are: if $(X,E,\tau )$ is $\tilde{I}$% -soft normal space and $(X,E,\tau ^{\ast })$ is $R_{0}^{^{\prime }}$-space, then there exists $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ such that $\tau ^{\ast }=\tau _{\delta _{\tilde{I}}}$. Also the soft topology generated by $\tilde{I}$-basic proximity of soft sets is finer than the soft topology generated by $R_{0}^{^{\prime }}$-$\check{C}$ech closure operator of soft sets. Finally, for a bijective soft map $% f:(X,E_{1})\rightarrow (Y,E_{2},\delta _{f(\tilde{I})}),$ we construct the largest $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ on $(X,E_{1})$ such that $f$ is $\tilde{I}$-proximally soft continuous mapping.
참고문헌 (34)
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