Abstract
We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element[Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology τ and the intuitionistic smooth topology ŋ generated by level fuzzy topologies with respect to τ [Theorem 3.10].
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