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Domain representations of spaces of compact subsets

Published online by Cambridge University Press:  25 March 2010

ULRICH BERGER ,
JENS BLANCK  and
PETTER KRISTIAN KØBER
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
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 2: Domains , April 2010 , pp. 107 - 126
Copyright
Copyright © Cambridge University Press 2010

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