Domain representability of certain function spaces

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let Cp (X) be the space of all continuous real-valued functions on a space X, with the topology of pointwise convergence. In this paper we show that Cp (X) is not domain representable unless X is discrete for a class of spaces that includes all pseudo-radial spaces and all generalized ordered spaces. This is a first step toward our conjecture that if X is completely regular, then Cp (X) is domain representable if and only if X is discrete. In addition, we show that if X is completely regular and pseudonormal, then in the function space Cp (X), Oxtoby's pseudocompleteness, strong Choquet completeness, and weak Choquet completeness are all equivalent to the statement "every countable subset of X is closed".

Original languageEnglish
Pages (from-to)1937-1942
Number of pages6
JournalTopology and its Applications
Volume156
Issue number11
DOIs
StatePublished - Jun 15 2009

Keywords

  • Domain representable space
  • Function space
  • Pointwise convergence topology
  • Pseudo-radial space
  • Pseudocomplete
  • Strongly Choquet complete
  • Transfinite sequence
  • Weakly Choquet complete

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