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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