Abstract Valuations: A Novel Representation of Plotkin Power Domain and Vietoris Hyperspace

Reinhold Heckmann


Abstract valuations on a topological space X are functions that map open sets to 0, 1, or one value in between. We define a space of abstract valuations which for a continuous dcpo X is homeomorphic to the Plotkin power domain of X, and for a Hausdorff 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.

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Reinhold Heckmann / heckmann@absint.com