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Domain representations of spaces of compact subsets

Published online by Cambridge University Press:  25 March 2010

ULRICH BERGER
Affiliation:
Department of Computer Science, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales Email: U.Berger@swan.ac.uk; j.e.blanck@swan.ac.uk
JENS BLANCK
Affiliation:
Department of Computer Science, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales Email: U.Berger@swan.ac.uk; j.e.blanck@swan.ac.uk
PETTER KRISTIAN KØBER
Affiliation:
Department of Mathematics, University of Oslo, Pb.1053 Blindern, N-0316 Oslo, Norway Email: petterk@math.uio.no

Abstract

We present a method for constructing from a given domain representation of a space X with underlying domain D, a domain representation of a subspace of compact subsets of X where the underlying domain is the Plotkin powerdomain of D. We show that this operation is functorial over a category of domain representations with a natural choice of morphisms. We study the topological properties of the space of representable compact sets and isolate conditions under which all compact subsets of X are representable. Special attention is paid to admissible representations and representations of metric spaces.

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Copyright
Copyright © Cambridge University Press 2010

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