FUZZY TOPOLOGIES OF SCOTT CONTINUOUS FUNCTIONS AND THEIR RELATION TO THE HYPERGRAPH FUNCTOR

Abstract

A new definition of the hypergraph functor from the category TOP(L) of L-fuzzy topological spaces to TOP is given which avoids the strictly less-than relation on L. For L a complete lattice with enough primes it will have all the earlier properties of the case when L is a complete chain. With L a continuous lattice, the functor ω_L which replaces the topology of a topological space by the L-topology consisting of all Scott continuous functions is discussed and some sufficient and necessary conditions for an L-fuzzy space to be in ω_L (TOP) are extended from L being the unit interval. Under this new approach the link between the hypergraph functor and the functor ω_L is preserved for L a distributive continuous lattice, i.e. a continuous lattice with enough primes.