Domain representability of Cp(X)

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let CP(X) be the space of continuous real-valued functions on X, with the topology of pointwise convergence. We consider the following three properties of a space X: (a) CP(X) is Scott-domain representable; (b) CP(X) is domain representable; (c) X is discrete. We show that those three properties are mutually equivalent in any normal TI-space, and that properties (a) and (c) are equivalent in any completely regular pseudo-normal space. For normal spaces, this generalizes the recent result of Tkachuk that Cp(X) is subcompact if and only if X is discrete.

Original languageEnglish
Pages (from-to)185-199
Number of pages15
JournalFundamenta Mathematicae
Volume200
Issue number2
DOIs
StatePublished - 2008

Keywords

  • Choquet complete
  • Domain
  • Domain representable space
  • Normal space
  • Pointwise convergence topology
  • Pseudo-normal space
  • Scott domain
  • Scott topology
  • Subcompact space

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