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A counterexample to the bounded orbit conjecture


Author: Stephanie M. Boyles
Journal: Trans. Amer. Math. Soc. 266 (1981), 415-422
MSC: Primary 54H25; Secondary 55M20, 58F25
DOI: https://doi.org/10.1090/S0002-9947-1981-0617542-9
MathSciNet review: 617542
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Abstract: A long outstanding problem in the topology of Euclidean spaces is the Bounded Orbit Conjecture, which states that every homeomorphism of $ {E^2}$ onto itself, with the property that the orbit of every point is bounded, must have a fixed point. It is well known that the conjecture is true for orientation preserving homeomorphisms. We provide a counterexample to the conjecture by constructing a fixed point free orientation reversing homeomorphism which satisfies the hypothesis of the conjecture.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0617542-9
Keywords: Fixed point free homeomorphism, bounded orbits, orientation preserving, orientation reversing
Article copyright: © Copyright 1981 American Mathematical Society

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