ON FUZZY TOPOLOGIES GENERATED BY FUZZY RELATIONS

ON FUZZY TOPOLOGIES GENERATED BY FUZZY RELATIONS

S. Mishra, R. Srivastava

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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 sucient conditions under which this fuzzy topology becomes fuzzy T0, fuzzy T1 and fuzzy T2. We have also introduced `nite intersection property (F.I.P.)' for fuzzy topological spaces and shown that in a fuzzy topological space (X;  ), this property is equivalent to the Lowen's fuzzy compactness. We have also obtained a sucient con- dition under which a fuzzy topology generated by a fuzzy relation becomes fuzzy compact.

Keywords

Fuzzy topology, fuzzy relation, separation axioms, fuzzy compactness.