Abstract
We introduce a new type of dcpo-completion of posets, called D -completion. For any poset P , the D -completion exists, and P and its D -completion have the isomorphic Scott closed set lattices. This completion is idempotent. A poset P is continuous (algebraic) if and only if its D -completion is continuous(algebraic). Using the D -completion, we construct the local dcpo-completion of posets, that revises the one given by Mislove. In the last section, we define and study bounded sober spaces.
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