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This paper reviews the one-to-one correspondence between stably compact spaces (a topolog-ical concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of real-valued functions on these spaces. This is the basis for transferring methods and results from functional analysis to… (More)

1 Introduction

We present domain-theoretic models that support both probabilistic and nondeterministic choice. In [36], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domain-theoretic tools. We present a model also using domain theory in the… (More)

In order to give the book under review the right appreciation it is necessary to first say a few words about its predecessor, the monograph A Compendium of Continuous Lattices which was published by the same six authors in 1980. The Compendium, as it is commonly called, contains a rather complete and very readable account of the theory of continuous… (More)

In this article we study a type of directed completion for posets and T 0-spaces introduced by O. Wyler [Wy81] that we call the D-completion. The category D of monotone convergence spaces is a full reflective subcategory of the category of topologi-cal spaces and continuous maps, and the D-completion gives the reflection of a topological space into D, and… (More)

We revisit extension results from continuous valuations to Radon measures for bifinite domains. In the framework of bifinite domains, the Prokhorov theorem (existence of projective limits of Radon measures) appears as a natural tool, and helps building a bridge between Measure theory and Domain theory. The study we present also fills a gap in the literature… (More)

We establish Choquet-Kendall-Matheron theorems on non-Hausdorff topological spaces. This typical result of random set theory is profitably recast in purely topological terms, using intuitions and tools from domain theory. We obtain three variants of the theorem, each one characterizing distributions, in the form of continuous valuations, over relevant… (More)

For the semantics of probabilistic features in programming mainly two approaches are used for building models. One is the Giry monad of Borel probability measures over metric spaces, and the other is Jones' probabilistic powerdomain monad [6] over dcpos (directed complete partial orders). This paper places itself in the second domain theoretical tradition.… (More)