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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost periodic homeomorphisms and $ p$-adic transformation groups on compact $ 3$-manifolds


Author: Joo S. Lee
Journal: Proc. Amer. Math. Soc. 121 (1994), 267-273
MSC: Primary 57M60; Secondary 57S20, 57S25
MathSciNet review: 1233977
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Abstract: In this paper we prove that regularly almost periodic is equivalent to nearly periodic for homeomorphisms on compact metric spaces and give an example to show that the above is false without the compactness assumption. We also prove that the following statement is equivalent to the Hilbert-Smith conjecture on compact 3-manifolds $ {M^3}$: If h is almost periodic on $ {M^3}$, with h = identity on $ \partial {M^3}$, then h = identity on $ {M^3}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1233977-2
PII: S 0002-9939(1994)1233977-2
Keywords: Manifold, almost periodic homeomorphism, the Hilbert-Smith conjecture
Article copyright: © Copyright 1994 American Mathematical Society