A note on perfect generalized ordered spaces

Harold R. Bennett, Masami Hosobuchi, David J. Lutzer

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper we examine certain recent generalizations of the topological property "X is perfect," i.e., closed subsets of X are Gδ-sets, to determine which are equivalent to being perfect in the category of generalized ordered spaces. We use these results to give necessary and sufficient conditions for X* and L(X), the two most common linearly ordered extensions of the generalized ordered space A, to be perfect.

Original languageEnglish
Pages (from-to)1195-1207
Number of pages13
JournalRocky Mountain Journal of Mathematics
Volume29
Issue number4
DOIs
StatePublished - 1999

Keywords

  • Almost perfect
  • Generalized ordered space
  • Linearly ordered space
  • Monotonically normal space
  • Perfect space
  • S-normality
  • Strongly densely normal
  • Weakly perfect space

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