Totally bounded ultrametric spaces generated by labeled rays

2024/02/24 by Dovgoshey, Oleksiy, Vito, Valentino · 6 citations
#FOS: Mathematics #General Topology (math.GN) #Primary 54E35 #Secondary 54E4

paper · doi:10.48550/arxiv.2402.15774

Abstract

We will say that an infinite tree T is almost a ray if T is the union of a ray and a finite tree. Let l be a non-degenerate labeling of the vertex set V of almost a ray T and let d_l be the corresponding ultrametric on V. It is shown that the ultrametric space (V, d_l) is totally bounded iff this space contains an infinite totally bounded subspace. We also prove that the last property characterizes the almost rays.

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• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• The Gomory-Hu inequality and trees
• Center of distances of ultrametric spaces generated by labeled trees

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