The Probabilistic Powerdomain for Stably Compact Spaces via Compact Ordered Spaces
نویسندگان
چکیده
منابع مشابه
The Probabilistic Powerdomain for Stably Compact Spaces via Compact Ordered Spaces
Stably compact spaces Xs can be described as being derived from compact ordered spaces X by weakening their topology to the open upper sets. In this paper the probabilistic powerdomain of a stably compact space Xs is investigated using the compact ordered space X and classical tools from measure theory and functional analysis. This allows to derive in a unified and elegant way known and new res...
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This paper reviews the one-to-one correspondence between stably compact spaces (a topological 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 the non-Hausdorff setting. As an applic...
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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. The probabilistic powerdomain monad is...
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We put forward a revised definition of stably compact spaces which allows us to show their equivalence with Nachbin’s compact ordered spaces in an entirely elementary fashion. We then exhibit some constructions for stably compact spaces which apparently have not appeared in the literature before. These constructions allow us to show that the set of (sub-)probability valuations can be equipped w...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2004
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2004.10.002