Domain representations of spaces of compact subsets

  • Authors:

  • Ulrich Berger;Jens Blanck;Petter kristian KØ/ber

  • Affiliations:

  • Department of computer science, swansea university, singleton park, swansea, sa2 8pp, wales email: u.berger@swan.ac.uk/ j.e.blanck@swan.ac.uk;Department of computer science, swansea university, singleton park, swansea, sa2 8pp, wales email: u.berger@swan.ac.uk/ j.e.blanck@swan.ac.uk;Department of mathematics, university of oslo, pb.1053 blindern, n-0316 oslo, norway email: petterk@math.uio.no

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2010

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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.