Domain representations of spaces of compact subsets
Ulrich Berger, Jens Blanck, Petter Kristian Køber · Mathematical Structures in Computer Science · 2010
We present a method for constructing from a given domain representation of a spaceXwith underlying domainD, a domain representation of a subspace of compact subsets ofXwhere the underlying domain is the Plotkin powerdomain ofD. 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 ofXare representable. Special attention is paid to admissible representations and representations of metric spaces.