Degrees of countable compactness and the Lindelöf property of L-fuzzy sets

In this paper, we introduce the notions of the degrees of countable compactness and the Lindelöf property in L-fuzzy topological spaces. Most of elementary results related to countable compactness and the Lindelöf property in general topology can be extended to L-fuzzy topological spaces. Moreover, many characterizations of the degrees of countable compactness and the Lindelöf property are presented.