The small boundary property in products
Abstract
For a continuous action G ↷ X G\curvearrowright X of a countable group on a compact metrizable space we show that the following are equivalent: (i) the action G ↷ X G\curvearrowright X has the small boundary property and no finite orbits, (ii) for every continuous action H ↷ Y H\curvearrowright Y of a countable group on a compact metrizable space, the product action G × H ↷ X × Y G\times H\curvearrowright X\times Y has the small boundary property. In particular, (ii) is automatic when X X is infinite and the action G ↷ X G\curvearrowright X is minimal and has the small boundary property. The argument relies on a small boundary version of the Urysohn lemma.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Mathematical Modeling in Engineering
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4219–4231
- Publication date
- 15 April 2026
- Language
- EN