The regular spaces with countably based models

AbstractThe regular spaces which may be realized as the set of maximal elements in an ω-continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces. These results enable us to prove that the probabilistic powerdomain of a countably based model of a metric space always contains a copy of the normalized Borel measures in their weak topology, and to establish the hierarchy for countably based models