Abstract

In this paper, we introduce the concepts of the degrees of compactness, countable compactness and Lindelof property in L-fuzzy pretopological spaces by means of implication operator. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. The notions of pre-compactness and semi-compactness in L-fuzzy topological spaces can be viewed as special cases of compactness in L-fuzzy pretopological spaces. Their properties are investigated. Further when L is completely distributive, their characterizations are presented.

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