Local homogeneity in fuzzy topological spaces

is also a fuzzy lattice. Throughout this paper, if {λj : j ∈ J} is a collection of L-sets in X , then (∨λj)(x) = ∨{λj(x) : j ∈ J}, x ∈ X ; and (∧λj)(x)=∧{λj(x) : j ∈ J}, x ∈ X . If r ∈ L, then rX denotes the fuzzy set given by rX(x) = r for all x ∈ X ; that is, rX denotes the “constant” L-set of level r, that is, the smallest and the largest elements of LX are denoted, respectively, by 0X and 1X . If rX is a constant L-set and λ ∈ LX , then rX ∧ λ will be denoted by rλ. λ∈ LX is called an L-crisp subset on X if there exists an ordinary subset A⊆ X such that λ= χA : X → {0,1} ⊆ L, that is, if λ is a characteristic function of some ordinary subset of X . An L-point on X is an L-subset xa ∈ LX defined as follows: