Local structure of homogeneous $ANR$-spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917738889347072 |
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| author | Valov, Vesko |
| author_facet | Valov, Vesko |
| contents | We investigate to what extend finite-dimensional homogeneous locally compact $ANR$-spaces have common properties with Euclidean manifolds. Specially, the local structure of homogeneous $ANR$-spaces is described. Using that description, we provide a positive solution of the problem whether every finite-dimensional homogeneous metric $ANR$-compactum $X$ is dimensionally full-valued, i.e. $\dim X\times Y=\dim X+\dim Y$ for any metric compactum $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10205 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local structure of homogeneous $ANR$-spaces Valov, Vesko General Topology Geometric Topology Primary 54C55, Secondary 55M15 We investigate to what extend finite-dimensional homogeneous locally compact $ANR$-spaces have common properties with Euclidean manifolds. Specially, the local structure of homogeneous $ANR$-spaces is described. Using that description, we provide a positive solution of the problem whether every finite-dimensional homogeneous metric $ANR$-compactum $X$ is dimensionally full-valued, i.e. $\dim X\times Y=\dim X+\dim Y$ for any metric compactum $Y$. |
| title | Local structure of homogeneous $ANR$-spaces |
| topic | General Topology Geometric Topology Primary 54C55, Secondary 55M15 |
| url | https://arxiv.org/abs/2303.10205 |