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Zbl 0587.54010
Katsaras, A.K.
On fuzzy syntopogenous structures.
(English)
[J] Rev. Roum. Math. Pures Appl. 30, 419-431 (1985). ISSN 0035-3965

Fuzzy syntopogenous structures generated on a set X are studied, If $R\sb{\phi}$ is the fuzzy real line then the families $S\sb R=\{<\sb{\epsilon}:\epsilon >0\}$ and $S\sb L=\{<\sp C\sb{\rho}:\epsilon >0\}$ are biperfect fuzzy syntopogenous structures on $R\sb{\phi}$. A fuzzy ordering family $\omega$ of bounded functions from a set X to R is defined and investigated. The family $S\sb{\omega}=\{<\sb{\omega,\epsilon}:\epsilon >0\}$ 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 $\tau =\tau (S\sb{\omega})$ 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 $f(y)(0+)\le \mu (y)$ for all $y\in X$.
MSC 2000:
*54A40 Fuzzy topology
54A15 Syntopogeneous structures

Keywords: Fuzzy syntopogenous structures

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