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Some questions of Arhangel'skii on rotoids

Volume 216 / 2012

Harold Bennett, Dennis Burke, David Lutzer Fundamenta Mathematicae 216 (2012), 147-161 MSC: Primary 54H11; Secondary 54B05, 54F05, 54H10. DOI: 10.4064/fm216-2-5

Abstract

A rotoid is a space $X$ with a special point $e \in X$ and a homeomorphism $F: X^2 \rightarrow X^2$ having $F(x,x) = (x,e)$ and $F(e,x) = (e,x)$ for every $x \in X$. 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.

Authors

  • Harold BennettMathematics Department
    Texas Tech University
    Lubbock, TX 79409, U.S.A.
    e-mail
  • Dennis BurkeMathematics Department
    Miami University
    Oxford, OH 45056, U.S.A.
    e-mail
  • David LutzerMathematics Department
    College of William and Mary
    Williamsburg, VA 23187, U.S.A.
    e-mail

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