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Compactness in fuzzy topological spaces. (English) Zbl 0576.54008
We introduce two kinds of new fuzzy compactness, the fuzzy \({\mathbb{Q}}_{\alpha}\)-compactness and the fuzzy strong \({\mathbb{Q}}\)- compactness, based upon the concepts of \({\mathbb{Q}}\)-neighborhoods and convergence of nets. They may be characterized not only in terms of finite \({\mathbb{Q}}\)-cover, but in terms in convergence of nets as well. They have many good properties and their definitions do not concern the topological structure of the value set [0,1].

MSC:
54A40 Fuzzy topology
54D30 Compactness
54E15 Uniform structures and generalizations
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