Domain representability and the Choquet game in Moore and BCO-spaces

H. R. Bennett, D. J. Lutzer, G. M. Reed

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

In this paper we investigate the role of domain representability and Scott-domain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α (= the nonempty player) in the strong Choquet game Ch (X); the existence of a stationary winning strategy for player α in Ch (X); and Rudin completeness. We note that a metacompact Čech-complete Moore space described by Tall is not Scott-domain representable and also give an example of Čech-complete separable Moore space that is not co-compact and hence not Scott-domain representable. We conclude with a list of open questions.

Original languageEnglish
Pages (from-to)445-458
Number of pages14
JournalTopology and its Applications
Volume155
Issue number5
DOIs
StatePublished - Jan 15 2008

Keywords

  • Base of countable order
  • Choquet completeness
  • Co-compact space
  • Domain representable
  • Moore space
  • Motonically complete base of countable order
  • Normality in Moore spaces
  • Rudin complete
  • Scott-domain representable
  • Stationary strategy
  • Strong Choquet game
  • Čech-complete

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