On Fuzzy Topologies Generated by Fuzzy Relations

Abstract

In this paper, we have introduced a fuzzy topology generated by a fuzzy relation as a generalization of the corresponding concept given by Smithson and ob-tained sufficient conditions under which this fuzzy topology becomes fuzzy T0, fuzzy T1and fuzzy T2. We have also introduced ‘finite intersection property (F.I.P.)’ for fuzzy topological spaces and shown that in a fuzzy topological space (X; τ ), this property is equivalent to the Lowen's fuzzy compactness. We have also obtained a sufficient con- dition under which a fuzzy topology generated by a fuzzy relation becomes fuzzy compact. ©Ișık University, Department of Mathematics, 2021; all rights reserved.