Some questions of Arhangel'skii on rotoids

Harold Bennett; Dennis Burke; David Lutzer

doi:10.4064/fm216-2-5

Some questions of Arhangel'skii on rotoids

Harold Bennett, Dennis Burke, David Lutzer

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	147-161
Number of pages	15
Journal	Fundamenta Mathematicae
Volume	216
Issue number	2
DOIs	https://doi.org/10.4064/fm216-2-5
State	Published - 2012

Keywords

Metrizable space
Michael line
Rotoid
Sorgenfrey line
η -set

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10.4064/fm216-2-5

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