Abstract
In 1986, Badard introduced the concept of a smooth topological space as a generalization of a classical as well as a Chang fuzzy topology. In this paper we introduce the notions of smooth interior and smooth closure of a fuzzy set and we derive some of their structural properties. Secondly the concepts subspace, smooth compactness, smooth almost compactness, and smooth near compactness are introduced and studied in the general framework of smooth topological spaces.
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