Given a poset P , the set, Γ(P), of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Pos d (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P) ∼ = Γ(Q) implies P ∼ = Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Pos d is ...

We show that a measurement μ on a continuous dcpo D extends to a measurement μ̄ on the convex powerdomain CD iff it is a Lebesgue measurement. In particular, kerμ must be metrizable in its relative Scott topology. Moreover, the space ker μ̄ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of kerμ, i.e., the space of nonempty compact subsets of kerμ in its Vietoris topolog...

Rios and Selinger have recently proposed a categorical model for the quantum programming language Proto-Quipper-M, which is an important fragment of the Quipper language. In this work, we describe an extension to their categorical model with the additional property that it is DCPOenriched, bringing us closer to modeling general recursion in the language. Similar to their model, our model exhibi...

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily-sequential functionals is not ω-complete (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a potentially wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF = PCF + pif (parallel if). Here we will present ...

A model of a space X is simply a continuous dcpo D and a homeomorphism : X ! max D, where max D is given its inherited Scott topology. We show that a space has a coherent model ii it has a Scott domain model and investigate the topological structure of spaces which have G models.

Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on topologies, is the same thing as the process of recovering a discrete poset from its algebraic dcpo (ideal completion).

As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily sequential functionals is not ω-complete and therefore not continuous in the traditional terminology (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF ...

We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense first introduced by Choquet.

This paper sets two goals. The first is to present algebraists with a purely order-theoretic derivation of the adjunction between the category DCPO of DCPOs (directed complete posets) and the category Frm of frames. This adjunction restricts to several Stone-type dualities which are well-known and of considerable interest to computer scientists. The second goal is to describe the object classes...

In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilatti...