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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multi-invariant sets on compact abelian groups


Author: Daniel Berend
Journal: Trans. Amer. Math. Soc. 286 (1984), 505-535
MSC: Primary 22D40; Secondary 11J61, 11J69
MathSciNet review: 760973
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Abstract: Let $ G$ be a finite-dimensional connected compact abelian group. Generalizing previous results, dealing with the case of finite-dimensional tori, a full characterization is given herewith of those commutative semigroups $ \Sigma $ of continuous endomorphisms of $ G$ which satisfy the following property: The only infinite closed $ \Sigma $-invariant subset of $ G$ is $ G$ itself.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0760973-X
PII: S 0002-9947(1984)0760973-X
Keywords: Flow, multi-parameter flow, $ \mathcal{F}$-flow, minimal flow, invariant set, solenoid, finite-dimensional group, semigroup of endomorphisms, ergodic endomorphism
Article copyright: © Copyright 1984 American Mathematical Society