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


54A40 Fuzzy topology
54A15 Syntopogeneous structures