Some questions of Arhangel'skii on rotoids

Harold Bennett, Dennis Burke, David Lutzer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A rotoid is a space X with a special point e 2 X and a homeomorphism F : X 2 → X 2 having F(x; x) = (x; e) and F(e; x) = (e; x) for every x 2 X. If any point of X can be used as the point e, then X is called a strong rotoid. We study some general properties of rotoids and prove that the Sorgenfrey line is a strong rotoid, thereby answering several questions posed by A. V. Arhangel'skii, and we pose further questions.

Original languageEnglish
Pages (from-to)147-161
Number of pages15
JournalFundamenta Mathematicae
Volume216
Issue number2
DOIs
StatePublished - 2012

Keywords

  • Metrizable space
  • Michael line
  • Rotoid
  • Sorgenfrey line
  • η -set

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