The coarse classification of homogeneous ultra-metric spaces

Taras Banakh, Ihor Zarichnyy

We prove that two homogeneous ultra-metric spaces $X,Y$ are coarsely equivalent if and only if ${\mathrm{Ent}}^{♯}(X)={\mathrm{Ent}}^{♯}(Y)$ where ${\mathrm{Ent}}^{♯}(X)$ is the…