1Mathematics Department Texas Tech University Lubbock, TX 79409, U.S.A. 2Mathematics Department Miami University Oxford, OH 45056, U.S.A. 3Mathematics Department College of William and Mary Williamsburg, VA 23187, U.S.A.
Fundamenta Mathematicae, Tome 216 (2012) no. 2, pp. 147-161
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.
Keywords:
rotoid space special point homeomorphism rightarrow having every point point called strong rotoid study general properties rotoids prove sorgenfrey line strong rotoid thereby answering several questions posed nbsp nbsp arhangelskii pose further questions
Affiliations des auteurs :
Harold Bennett
1
;
Dennis Burke
2
;
David Lutzer
3
1
Mathematics Department Texas Tech University Lubbock, TX 79409, U.S.A.
2
Mathematics Department Miami University Oxford, OH 45056, U.S.A.
3
Mathematics Department College of William and Mary Williamsburg, VA 23187, U.S.A.
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Harold Bennett; Dennis Burke; David Lutzer. Some questions of Arhangel'skii on rotoids. Fundamenta Mathematicae, Tome 216 (2012) no. 2, pp. 147-161. doi: 10.4064/fm216-2-5
