Multi-invariant sets on compact abelian groups

Berend, Daniel

doi:10.1090/S0002-9947-1984-0760973-X

Multi-invariant sets on compact abelian groups
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Trans. Amer. Math. Soc. 286 (1984), 505-535 Request permission

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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Modern algebra