In this paper, we introduce the notion of L-ideal in L-set theory.Also we introduce the concept of L-local function.These concepts are discussed with a view to find new L-topologies from the original one. The basic structure, especially a basis for such generated L-topologies also studied here. The notion of L-compatibility of L-ideals with L-topologies is introduced and some equivalent conditions concerning this topic are established here.Moreover, by using L-local function we introduce L-operator ψsatisfying ψ(A_L) = 1X– (1X–A_L)*,for allA_L⊆LXand we discuss some characterizations this L-operator by use L-open sets.
