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The N-compactness in L-fuzzy topological spaces. (English) Zbl 0639.54006
While the problem of defining compactness in fuzzy topological spaces would seem trivial, the formal generalization has many deficiencies. For example, there is no Tikhonov theorem and a one point set need not be fuzzy compact. Even the widely used fuzzy compactness of Lowen and the strong fuzzy compactness of Gantner, Steinlage, and Warren are not necessarily inherited by fuzzy closed subsets. Guojun Wang [J. Math. Anal. Appl. 94, 1-23 (1983; Zbl 0512.54006)] introduced N- compactness to overcome this problem and showed it equivalent to fuzzy and strong fuzzy compactness under a \(T_ 2\)-like separation axiom. The present paper extends Wang’s work from [0,1] to arbitrary L-fuzzy topological spaces and gives a “geometrical” characterization of N- compactness.
Reviewer: L.M.Friedler

MSC:
54A40 Fuzzy topology
54D30 Compactness
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References:
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