Go-spaces with ω-closed discrete dense subsets

Harold R. Bennett, Robert W. Heath, David J. Lutzer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this paper we study the question "When does a perfect generalized ordered space have a ω-closed-discrete dense subset?" and we characterize such spaces in terms of their subspace structure, s-mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a ω-closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.

Original languageEnglish
Pages (from-to)931-939
Number of pages9
JournalProceedings of the American Mathematical Society
Volume129
Issue number3
DOIs
StatePublished - 2001

Keywords

  • G-diagonal
  • Generalized ordered space
  • Linearly ordered space
  • Metrization
  • Perfect, ω-discrete dense subset
  • Souslin line
  • Weak monotone ortho-base

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