Some Results on Poset Models Consisting of Compact Saturated Subsets

Abstract Given a topological space X, the set Q ( X ) of all nonempty saturated compact subsets of X is a poset with respect to the reverse inclusion order. The posets of the form Q ( X ) play important roles in several aspects of domain theory. In this paper, we investigate some further properties of such posets, in particular their links to the dcpo models of T 1 topological spaces.