Completeness and compactness of quantitative domains

Authors:
Paweł Waszkiewicz
Affiliations:
Jagiellonian University, Kraków, Poland
Venue:
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Year:
2005

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Abstract

In this paper we study the interplay between metric and order completeness of semantic domains equipped with generalised distances. We prove that for bounded complete posets directed-complete- ness and partial metric completeness are interdefinable. Moreover, we demonstrate that Lawson-compact, countably based domains are precisely the compact pmetric spaces that are continuously ordered.