In this paper we use fuzzy˛-sets in order to obtain certain characterizations and properties of upper (or lower) fuzzy˛-continuous multifunctions.

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The purpose of this paper is to provide a new class of generalized N−preopen sets, namely, regular generalized N−preopen sets which is finer than the class of regular generalized preopen sets and the class of regular generalized open sets. Furthermore, we study the fundamental topological properties and introduce the notion of regular generalized N−precontinuous functions.