Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866929302454403072 |
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| author | Ceccherini-Silberstein, Tullio Coornaert, Michel |
| author_facet | Ceccherini-Silberstein, Tullio Coornaert, Michel |
| contents | We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every pre-injective continuous self-mapping of $X$ commuting with the action of $G$ on $X$ is surjective. This extends a result previously obtained by Hanfeng Li in the case when $X$ is metrizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_02740 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property Ceccherini-Silberstein, Tullio Coornaert, Michel Dynamical Systems 54E15, 37B05, 37B10, 37B15, 37B40, 43A07, 68Q80 We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every pre-injective continuous self-mapping of $X$ commuting with the action of $G$ on $X$ is surjective. This extends a result previously obtained by Hanfeng Li in the case when $X$ is metrizable. |
| title | Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property |
| topic | Dynamical Systems 54E15, 37B05, 37B10, 37B15, 37B40, 43A07, 68Q80 |
| url | https://arxiv.org/abs/1905.02740 |