On Extensions over Semigroups and Applications

Applying a theorem according to Rhemtulla and Formanek, we partially solve an open problem raised by Hochman with an affirmative answer. Namely, we show that if G is a countable torsion-free locally nilpotent group that acts by homeomorphisms on X, and S ⊂ G is a subsemigroup not containing the unit of G such that f ∈ 〈 1, s f: s ∈ S 〉 for every f ∈ C ( X ), then ( X, G ) has zero topological entropy.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.