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Finite-to-one fuzzy maps and fuzzy perfect maps

In this paper we define, for fuzzy topology, notions corresponding to finite-to-one and k-to-one maps. We study the relationship between these new fuzzy maps and various kinds of fuzzy perfect maps. Also, we show the invariance and the inverse inveriance under the various kinds of fuzzy perfect maps (and the finite-to-one fuzzy maps), of different properties of fuzzy topological spaces.