On Some Ordinary and Fuzzy Homogenity Types

Finite SLH topological spaces are characterized as partition topological spaces. As a consequence, two partial answers for a question raised in [3] are obtained. Closed-homogeneous topological spaces are characterized. Having a minimal open set is proved to be a sufficient condition for a homogeneous topological space to be closed-homogeneous. Closed-homogeneity is extended to include fuzzy topological spaces as a “good extension” according to Lowen’s sense of closed-homogeneity in ordinary topological spaces. It is proved that homogeneity and closed-homogeneity in fuzzy topological spaces are equivalent under some conditions. Various open questions are also given.