Some questions of Arhangel'skii on rotoids
Volume 216 / 2012
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.
