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

Lee, Joo S.

doi:10.1090/S0002-9939-1994-1233977-2

Almost periodic homeomorphisms and $p$-adic transformation groups on compact $3$-manifolds
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by Joo S. Lee

Proc. Amer. Math. Soc. 121 (1994), 267-273

DOI: https://doi.org/10.1090/S0002-9939-1994-1233977-2

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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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