Abstract valuations: A novel representation of Plotkin power domain and Vietoris hyperspace

valuations on a topological space X are functions that map open sets to 0, 1, or one value in between. We deene a space of abstract valuations which for a continuous dcpo X is homeomorphic to the Plotkin power domain of X, and for a Hausdorr space X yields the Vietoris hyperspace of X. Thus we obtain a novel concrete representation of the Plotkin power domain. This representation is more similar to the standard representation of the probabilistic power domain than the previously known ones.