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On a fuzzy topological structure. (English) Zbl 0638.54007
The author introduces a generalization of fuzzy topology and relates it to previously studied notions through the categorical framework introduced by S. E. Rodabaugh [Fuzzy Sets Syst. 9, 241-265 (1983; Zbl 0527.54005)]. The author’s structures are fuzzy subsets of I X instead of the crisp subcollections usually studied. He develops a category of such structures and introduces several functors - for example, a generalization of Lowen’s \(\omega\) construction. Lastly, he defines a degree of compactness, announces several results without proof, and states a related unsolved problem.
Reviewer: A.J.Klein

54A40 Fuzzy topology
54B30 Categorical methods in general topology