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 |
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Pages (from-to) | 147-161 |
Number of pages | 15 |
Journal | Fundamenta Mathematicae |
Volume | 216 |
Issue number | 2 |
DOIs | |
State | Published - 2012 |
Keywords
- Metrizable space
- Michael line
- Rotoid
- Sorgenfrey line
- η -set