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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)

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 his foundation of probability theory, Bruno de Finetti devised a betting scheme where a bookmaker offers bets on the outcome of events φ occurring in the future. He introduced a criterion for coherent bookmaking, and showed that coherent betting odds are given by some probability distribution. While de Finetti dealt with yes-no events and boolean… (More)

- KLAUS KEIMEL
- 2005

The theme of this paper is the extension of continuous valuations on the lattice of open sets of a T 0-space to Borel measures. A general extension principle is derived that provides a unified approach to a variety of extension theorems including valuations that are directed suprema of simple valuations, continuous valuations on locally compact sober… (More)

- Klaus Keimel
- 2008

The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the… (More)

- Klaus Keimel
- 1998

For partially ordered sets that are continuous in the sense of D. S. Scott, the way-below relation is crucial. It expresses the approximation of an ideal element by its nite parts. We present explicit characterizations of the way-below relation on spaces of continuous functions from topological spaces into continuous posets. Although it is well-known in… (More)

Already in his PhD Thesis on compact Abelian semigropups under the direction of Karl Hein-rich Hofmann the author was lead to investigate locally compact cones [18]. This happened in the setting of Hausdorff topologies. The theme of topological cones has been reappearing in the author's work in a non-Hausdorff setting motivated by the needs of mathematical… (More)