A new definition of the hypergraph functor from the category TOP(L) ofL-fuzzy topological spaces to TOP is given which avoids the strictly less-than relation onL. ForLa complete latticewith enoughprimes it will have all the earlier properties of the case whenLis a complete chain. WithLa continuous lattice, the functor ωLwhich replaces the topology of a topological space by theL-topology consisting of all Scott continuous functions is discussed and some sufficient and necessary conditions for anL-fuzzy space to be in ωL(TOP) are extended fromLbeing the unit interval. Under this new approach the link between the hypergraph functor and the functor ωLis preserved forLa distributive continuous lattice, i.e. a continuous lattice with enough primes.