a duality between fuzzy domains and strongly completely distributive $l$-ordered sets

the aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. all values aretaken in a fixed frame $l$. a definition of (strongly) completelydistributive $l$-ordered sets is introduced. the main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $l$-orderedsets. the results in this paper establish close connections amongfuzzy-set approach of quantitative domains and fuzzy topology withmodified $l$-sober spaces and spatial $l$-frames as links. inaddition, some mistakes in [k.r. wagner, liminf convergence in$omega$-categories, theoretical computer science 184 (1997)61--104] are pointed out.