This paper,a new notion of J-compactness is introduced in L-fuzzy topological. It possesses the following properties: (1)J-compactnessis hereditary for J-closed subsets,(2)J-compactness is preserved underJ-irresolute mapping. (3)Every set with finite support is J-compactness. In this paper,a new notion of J-compactness is introduced in L-fuzzy to pological. It possesses the following properties: (1)J-compactnessis hereditary for J-closed subsets,(2)J-compactness is preserved under J-irresolute mapping. (3)Every set with finite support is J-compactness.
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