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In this paper we study the role of invertibility on homogeneity of a fuzzy topological space and vice-versa. In general invertibility and homogeneity need not imply each other. However there are situations under which one implies the other. If the invertible subspace is homogeneous, then it is proved that the parent fuzzy topological space is also homogeneous. We also investigate the properties of orbits in invertible fuzzy topological spaces and characterize them.
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