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 $S\subset G$ is a subsemigroup not containing the unit of G such that $f\in \langle 1,sf:s\in S\rangle$ for every $f\in C\left(X\right)$ , then $(X,G)$ has zero topological entropy. View Full-Text