A rotoid is a space X with a special point e ∈ X and a homeomorphism F: X² → X² having F(x,x) = (x,e) and F(e,x) = (e,x) for every x ∈ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-5,
author = {Harold Bennett and Dennis Burke and David Lutzer},
title = {Some questions of Arhangel'skii on rotoids},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {147-161},
zbl = {1245.54030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-5}
}
Harold Bennett; Dennis Burke; David Lutzer. Some questions of Arhangel'skii on rotoids. Fundamenta Mathematicae, Tome 219 (2012) pp. 147-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-5/