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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.14889 |
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| _version_ | 1866912493003079680 |
|---|---|
| author | Sipacheva, Ol'ga |
| author_facet | Sipacheva, Ol'ga |
| contents | Strongly zero-dimensional topological groups $G_1$, $G_2$, and $G$ such that $G_1\times G_2$ has positive covering dimension and $G$ contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of $G_1$ are Lindelöf and $G_2$ is second-countable. An example of a strongly zero-dimensional space $X$ whose free, free Abelian, and free Boolean topological groups have positive covering dimension is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups Sipacheva, Ol'ga General Topology 22A05, 54F45 Strongly zero-dimensional topological groups $G_1$, $G_2$, and $G$ such that $G_1\times G_2$ has positive covering dimension and $G$ contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of $G_1$ are Lindelöf and $G_2$ is second-countable. An example of a strongly zero-dimensional space $X$ whose free, free Abelian, and free Boolean topological groups have positive covering dimension is also given. |
| title | There are No Product and Subgroup Theorems for the Covering Dimension of Topological Groups |
| topic | General Topology 22A05, 54F45 |
| url | https://arxiv.org/abs/2507.14889 |