Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


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
MathSciNet review: 617542
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54H25, 55M20, 58F25

Retrieve articles in all journals with MSC: 54H25, 55M20, 58F25

Additional Information

PII: S 0002-9947(1981)0617542-9
Keywords: Fixed point free homeomorphism, bounded orbits, orientation preserving, orientation reversing
Article copyright: © Copyright 1981 American Mathematical Society