On dense subspaces of generalized ordered spaces

Harold R. Bennett, David J. Lutzer, Steven D. Purisch

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

In this paper we study four properties related to the existence of a dense metrizable subspace of a generalized ordered (GO) space. Three of the properties are classical, and one is recent. We give new characterizations of GO-spaces that have dense metrizable subspaces, investigate which GO-spaces can embed in GO-spaces with one of the four properties, and provide examples showing the relationships between the four properties.

Original languageEnglish
Pages (from-to)191-205
Number of pages15
JournalTopology and its Applications
Volume93
Issue number3
DOIs
StatePublished - 1999

Keywords

  • Baire Category Theorem
  • Dense metrizable subset
  • Dense σ-discrete subset
  • G-diagonal
  • GO-space
  • Lexicographic products
  • Linearly ordered space
  • Perfect spaces

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