2024/06/18 by Kerr, David, Li, Hanfeng
#Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2406.12697
For a continuous action G\curvearrowright X of a countable group on a compact metrizable space we show that the following are equivalent: (i) the action G\curvearrowright X has the small boundary property and no finite orbits, (ii) for every continuous action H\curvearrowright Y of a countable group on a compact metrizable space, the product action G× H\curvearrowright X× Y has the small boundary property. In particular, (ii) is automatic when G is infinite and the action G\curvearrowright X is minimal and has the small boundary property. The argument relies on a small boundary version of the Urysohn lemma.