Abstract
In this paper, β-compactness is introduced in L-topological spaces, where L is a fuzzy lattice. And its topological properties are systematically studied. This β-compactness is defined for arbitrary L-subsets. The intersection of a β-compact L-fuzzy subset and a β-closed L-fuzzy subset is β-compact with a good extension. Also different characterizations are obtained and some of its properties are studied.
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