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arXiv · 2511.03722

Uncountably many homogeneous real trees with the same valence

Pénélope Azuelos
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Abstract

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 $κ$.

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Pénélope Azuelos. 2025-11-05. Uncountably many homogeneous real trees with the same valence. https://arxiv.org/abs/2511.03722

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