bound in the subset.) In the literature, dcpos sometimes also appear under the label up-complete poset.

A pointed directed-complete partial order (pointed dcpo, sometimes abbreviated cppo), is a dcpo with a least element (usually denoted ). Formulated differently, a pointed dcpo has a supremum for every directed or empty subset. The term chain-complete partial order is also used, because of the characterization of pointed dcpos as posets in which every chain