Uncountably many homogeneous real trees with the same valence
For any cardinal κ ≥ 2, there is a unique complete real tree whose points all have valence κ. In this note, we show that, whenever κ ≥ 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.
Authors
- Pénélope Azuelos (ORCID: https://orcid.org/0009-0009-2310-050X)
Publication Details
- Journal
- International Journal of Algebra and Computation
- Published
- 2026-10-30
- DOI
- https://doi.org/10.1142/s0218196726500724
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00