The separability in L-Fuzzy topological space is further generalized by using the concepts of δ-open sets and δ-far-field.δTi-separability(i=-1,0,1,2,3,4)is defined and some equivalent characterizations of δTi-separability are studied,In addition,a series of good properties of δTi-separability,such as L-good generalization,heritability,multiplicability,homeomorphism invariance,LFδ-topological properties are proved,and proved the relationship between the δTi-separability of weakly induced L-Fuzzy topological spaces and the δTi-separability of their base spaces.The research results enrich and develop the theory of separability.
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