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

摘要

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 #x3C9;Lwhich 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 #x3C9;L(TOP) are extended fromLbeing the unit interval. Under this new approach the link between the hypergraph functor and the functor #x3C9;Lis preserved forLa distributive continuous lattice, i.e. a continuous lattice with enough primes.