A note on point-countability in linearly ordered spaces

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Abstract

In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a σ-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a σ-point-finite base is given. Conditions are given for the metrizability of a LOTS with a point-countable base and it is shown that a connected LOTS with a point-countable base is homeomorphic to a connected subset of the real line.

Original languageEnglish
Pages (from-to)598-606
Number of pages9
JournalProceedings of the American Mathematical Society
Volume28
Issue number2
DOIs
StatePublished - May 1971

Keywords

  • Linearly ordered spaces
  • Point-countable base
  • Quasi-developable space
  • σ-Pointfinite base

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