Ordered spaces with special bases

Harold Bennett, David Lutzer

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a Gδ-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.

Original languageEnglish
Pages (from-to)289-299
Number of pages11
JournalFundamenta Mathematicae
Volume158
Issue number3
StatePublished - 1999

Keywords

  • Generalized ordered space
  • Linearly ordered space
  • Metrizable space
  • Open-in-finite base
  • Point-countable base
  • Quasi-developable space
  • Sharp base
  • Weakly uniform base
  • ω-in-ω base

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