On a question of Maarten Maurice

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this note we give ZFC results that reduce the question of Maarten Maurice about the existence of σ-closed-discrete dense subsets of perfect generalized ordered spaces to the study of very special Baire spaces, and we discuss the current status of the question for spaces with small density. Work of Shelah, Todorčevic, Qiao, and Tall shows that Maurice's problem is undecidable for generalized ordered spaces of local density ω1.

Original languageEnglish
Pages (from-to)1631-1638
Number of pages8
JournalTopology and its Applications
Volume153
Issue number11
DOIs
StatePublished - May 1 2006

Keywords

  • Baire space
  • Density ω
  • First-category
  • GO-space
  • Heath's question
  • LOTS
  • Maurice's question
  • Nyikos' question
  • Perfect space
  • σ-discrete dense set

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