On Dense Subgroups of Homeo(I)
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arXiv
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866913022655594496 |
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| author | Akhmedov, Azer |
| author_facet | Akhmedov, Azer |
| contents | We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of $\mathrm{Homeo}_{+}(I)$ admits a faithful discrete representation in it. In the last section, we demonstrate that finitely generated dense subgroups have infinite girth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1312_1654 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On Dense Subgroups of Homeo(I) Akhmedov, Azer Group Theory Dynamical Systems Geometric Topology We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of $\mathrm{Homeo}_{+}(I)$ admits a faithful discrete representation in it. In the last section, we demonstrate that finitely generated dense subgroups have infinite girth. |
| title | On Dense Subgroups of Homeo(I) |
| topic | Group Theory Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/1312.1654 |