Domain-representable spaces

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domain-representable space, and that if X is domain-representable, then so is any Ga-subspace of X. It follows that any Čech-complete space is domain-representable. These results answer several questions in the literature.

Original languageEnglish
Pages (from-to)255-268
Number of pages14
JournalFundamenta Mathematicae
Volume189
Issue number3
DOIs
StatePublished - 2006

Keywords

  • Baire space
  • Choquet-complete space
  • Continuous dcpo
  • Domain
  • Domain-representable space
  • G -subspace
  • Michael line
  • Ordinal space
  • Scott domain
  • Sorgenfrey line
  • Čech-complete space

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