A metric space of a.h. stone and an example concerning σ-minimal bases

Harold R. Bennett, David J. Lutzer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we use a metric space V due to A. H. Stone and one of its completions X to construct a linearly ordered topological space E = E(Y,X) that is Čecil complete, has a tr-closed-discrete dense subset, is perfect, hereditarily paracompact, first-countable, and has the property that each of its subspaces has a σ-minimal base for its relative topology. However, E is not metrizable and is not quasi-developable. The construction of E(Y, X) is a point-splitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.

Original languageEnglish
Pages (from-to)2191-2196
Number of pages6
JournalProceedings of the American Mathematical Society
Volume126
Issue number7
DOIs
StatePublished - 1998

Keywords

  • Cech complete
  • Cr-minimal base
  • Generalized ordered space
  • Linearly ordered space
  • Metrization theory
  • Paracompact
  • Perfect space

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