… The dcpo-completion of a poset P is usually taken to be the ideal completion Id(P) … (P) to
poset P cannot be extended to a functor from the category POSd of posets and Scott continuous …

… which have been mentioned above, there is another special kind of posets in domain theory
… posets by doing a procedure called dcpocompletion. In the past, the dcpo-completion was …

… the so called continuous poset [3]. It was proved in [16] that if the dcpo-completion of a poset
\(P… Hence, by Corollary 19, the dcpo-completion of a continuous poset \(P\) is the poset of all …

… of continuity of posets, called θ-continuity. Topological characterizations of θ-continuous
posets are put forward. We also present two types of dcpo-completion of posets which are Dθ-…

… to a directed complete poset . It is thus natural to wonder what the dcpo - completion of $ C
… to the lattice of Scott closed sets of its dcpo - completion . We also prove that a topological …

… of directed complete posets for the assignment that sends a directed complete poset to its
Scott … directed complete posets. Some problems will be posed and elaborated for further work. …

… Completing, or directedly completing, posets may be done freely if we only consider one-…
σ obtained from the free co-dcpo followed by the dcpo completion described in this paper and …

… poset) the down-set of a directed complete poset? In addition it is shown that a poset P is a
… For bounded complete posets a similar result is obtained: they are exactly the down-sets of …

… A subset U of a poset P is Scott open if (i) U =↑U and (ii) for any directed subset D, … poset
P is directed complete if its every directed subset has a supremum. A directed complete poset …

… Jia and Mislove (2022) have considered the D-completion of Vf (X) with the weak topology
and dcpo completion of the poset Vf (X), which are different from our construction due to the …