Weak similarities of finite ultrametric and semimetric spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917881216761856 |
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| author | Petrov, Evgeniy |
| author_facet | Petrov, Evgeniy |
| contents | Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $Φ\colon X\to Y$. We find a structural characteristic of finite ultrametric spaces for which the isomorphism of its representing trees implies a weak similarity of the spaces. We also find conditions under which the Hasse diagrams of balleans of finite semimetric spaces are isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak similarities of finite ultrametric and semimetric spaces Petrov, Evgeniy General Topology 54E35, 05C05 Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $Φ\colon X\to Y$. We find a structural characteristic of finite ultrametric spaces for which the isomorphism of its representing trees implies a weak similarity of the spaces. We also find conditions under which the Hasse diagrams of balleans of finite semimetric spaces are isomorphic. |
| title | Weak similarities of finite ultrametric and semimetric spaces |
| topic | General Topology 54E35, 05C05 |
| url | https://arxiv.org/abs/2412.20539 |