Uncountably many homogeneous real trees with the same valence
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917062963625984 |
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| author | Azuelos, Pénélope |
| author_facet | Azuelos, Pénélope |
| contents | For any cardinal $κ\geq 2$, there is a unique complete real tree whose points all have valence $κ$. In this note, we show that, when $κ\geq 3$, it is necessary to assume completeness. More precisely, we show that there exist uncountably many homogeneous incomplete real trees whose points all have valence $κ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncountably many homogeneous real trees with the same valence Azuelos, Pénélope Metric Geometry For any cardinal $κ\geq 2$, there is a unique complete real tree whose points all have valence $κ$. In this note, we show that, when $κ\geq 3$, it is necessary to assume completeness. More precisely, we show that there exist uncountably many homogeneous incomplete real trees whose points all have valence $κ$. |
| title | Uncountably many homogeneous real trees with the same valence |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2511.03722 |