On exponential Lowen spaces

An L-fuzzy topological space (X, Δ) is called a Lowen space if Δ has a basis consisting of one-step functions, that is to say, the elements in Δ of the form a ∧ U, a ∈ L, U ⊆ X, is a basis for Δ.. In the case L = [0,1], (X, Δ) is a Lowen space if and only if (X, Δ) is a fuzzy neighborhood space in the sense of Lowen. By introducing some natural L-fuzzy topologies for function spaces it is proved that if 0 ∈ L is a prime then a Lowen space (X, Δ) is exponential in the construct of Lowen spaces provided that its open-set lattice is continuous. More specifically, a fuzzy neighbourhood space is exponential if its open-set lattice is continuous