Many for the Price of One Duality Principle for Affine Sets

Recently, D. Hofmann considered topological spaces as generalized orders, characterizing the ones, which satisfy a suitably defined topological analogue of the complete distributivity law. He showed that the category of distributive spaces is dually equivalent to a category of frames, since they both represent the idempotents split completion of the same category. This paper considers the duality of D. Hofmann in the setting of affine sets of Y. Diers.