On exponential Lowen spaces

An L-fuzzy topological space (X, /spl Delta/) is called a Lowen space if /spl Delta/ has a basis consisting of one-step functions, that is to say, the elements in /spl Delta/ of the form a /spl and/ U, a /spl isin/ L, U /spl sube/ X, is a basis for /spl Delta/.. In the case L = [0,1], (X, /spl Delta/) is a Lowen space if and only if (X, /spl Delta/) 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 /spl isin/ L is a prime then a Lowen space (X, /spl Delta/) 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.