Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.13203 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912055916756992 |
|---|---|
| author | Melleray, Julien |
| author_facet | Melleray, Julien |
| contents | We investigate some properties of the clopen type semigroup of an action of a countable group on a compact, $0$-dimensional, Hausdorff space X. We discuss some characterizations of dynamical comparison (most of which were already known in the metrizable case) in this setting; and prove that for a Cantor minimal action $α$ of an amenable group the topological full group of $α$ admits a dense, locally finite subgroup iff the corresponding clopen type semigroup is unperforated. We also discuss some properties of clopen type semigroups of the Stone-Čech compactifications and universal minimal flows of countable groups, and derive some consequences on generic properties in the space of minimal actions of a given countable group on the Cantor space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13203 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Clopen type semigroups of actions on $0$-dimensional compact spaces Melleray, Julien Dynamical Systems We investigate some properties of the clopen type semigroup of an action of a countable group on a compact, $0$-dimensional, Hausdorff space X. We discuss some characterizations of dynamical comparison (most of which were already known in the metrizable case) in this setting; and prove that for a Cantor minimal action $α$ of an amenable group the topological full group of $α$ admits a dense, locally finite subgroup iff the corresponding clopen type semigroup is unperforated. We also discuss some properties of clopen type semigroups of the Stone-Čech compactifications and universal minimal flows of countable groups, and derive some consequences on generic properties in the space of minimal actions of a given countable group on the Cantor space. |
| title | Clopen type semigroups of actions on $0$-dimensional compact spaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2210.13203 |