# zbMATH — the first resource for mathematics

On fuzzy syntopogenous structures. (English) Zbl 0587.54010
Fuzzy syntopogenous structures generated on a set X are studied, If $$R_{\phi}$$ is the fuzzy real line then the families $$S_ R=\{<_{\epsilon}:\epsilon >0\}$$ and $$S_ L=\{<^ C_{\rho}:\epsilon >0\}$$ are biperfect fuzzy syntopogenous structures on $$R_{\phi}$$. A fuzzy ordering family $$\omega$$ of bounded functions from a set X to R is defined and investigated. The family $$S_{\omega}=\{<_{\omega,\epsilon}:\epsilon >0\}$$ is a fuzzy syntopogenous structure on X. Let $$\tau$$ be a fuzzy topology on X and let $$\omega$$ be a fuzzy ordering family on X. Then $$\tau =\tau (S_{\omega})$$ iff two conditions are satisfied: (1) $$\omega$$ consists of $$\tau$$-upper semicontinuous functions. (2) If $$\mu\in \tau$$, $$x\in X$$ and $$\mu (x)>\vartheta$$ then there exists $$f\in \omega$$ with $$f(x)(1- 0)>\vartheta$$, and $$f(y)(0+)\leq \mu (y)$$ for all $$y\in X$$.
Reviewer: D.Adnadjević

##### MSC:
 54A40 Fuzzy topology 54A15 Syntopogeneous structures
##### Keywords:
Fuzzy syntopogenous structures