The small boundary property in products
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909226893312000 |
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| author | Kerr, David Li, Hanfeng |
| author_facet | Kerr, David Li, Hanfeng |
| contents | 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 $G\times H\curvearrowright X\times Y$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The small boundary property in products Kerr, David Li, Hanfeng Dynamical Systems Operator Algebras 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 $G\times H\curvearrowright X\times Y$ 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. |
| title | The small boundary property in products |
| topic | Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2406.12697 |