Daniel Berend

Given a compact metric group G, we are interested in those semigroups ∑of continuous endomorphisms of G, possessing the following property: The only infinite, closed, ∑-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization—for the case of finitedimensional tori—of those commutative semigroups with the aforementioned property.