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In this paper, the concepts of L-fuzzy countable compactness and the L-fuzzy Lindelof property are introduced in L-fuzzy topological spaces, where L is a completely distributive DeMorgan algebra. An L-fuzzy compact L-fuzzy set is L-fuzzy countably compact and has the L-fuzzy Lindelof property. An L-fuzzy set having the L-fuzzy Lindelof property is L-fuzzy countably compact if and only if it is L-fuzzy compact. Many characterizations of L-fuzzy countable compactness and the L-fuzzy Lindelof property are presented.

COUNTABLE COMPACTNESS AND THE LINDELOF PROPERTY IN L-FUZZY TOPOLOGICAL SPACES