Multi-invariant sets on compact abelian groups Academic Article uri icon


  • 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 Σ of continuous endomorphisms of G which satisfy the following property: The only infinite closed Σ-invariant subset of G is G itself.

publication date

  • January 1, 1984