I(L)-topological vector spaces and its level topological spaces

-topological groups and its level L-topological groups

“…Therefore 1−t (P ) ∈ − (x ). [11]). Let = { s } s∈I 1 be a co-tower of L-topologies on X, then the operator • : I (L) X → I (L) X defined by…”

“…Also, an I (L)-fuzzy set is ( )-open iff s ( ) ∈ s for all s ∈ I 1 . [11]). Suppose that (I (L) X , ( )) is an I (L)-topological space generated by a co-tower of L-topologies = { s } s∈I 1 on X.…”

“…The main purpose of this paper is to generalize the results in [11] to L-topological groups. We prove that for each co-tower of group Ltopologies = { s } s∈[0,1) on a group X, there exists an I (L)-topology ( ) on X, which is called the I (L)-topology generated by , such that (I (L) X , ( )) is an I (L)-topological group and s ( ( )) = s for each s ∈ [0, 1).…”

“…He [9] also obtained a necessary and sufficient condition for a chain of L-topological structures on a set X such that there exists an (not necessarily unique in general) I (L)-topological structure of which the level L-topological structures are exactly the given chain of L-topological structures. Inspired by Wang's work, Fang and Yan [2,11] introduced and studied the induced I (L)-topological vector spaces and supplied a new method to generate I (L)-topological vector spaces by a family of L-topological vector spaces.…”