Abstract
We continue the study of the dcpos which are determined by their Scott closed set lattices. Such dcpos are called Cσ-unique. Some new sufficient conditions for a dcpo to be Cσ-unique are given. One example is constructed to show that a Cσ-unique dcpo need not be dominated. Thus the question whether the dominated dcpos form a maximal Γ-faithful class of dcpos is negatively answered. Using a recent result by Zhao and Xi, we also deduce that every T1 topological space has a dcpo model that is Cσ-unique.
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