齐次超度量空间的粗分类
The coarse classification of homogeneous ultra-metric spaces
摘要：
证明了两个齐次超度量空间$X,Y$是粗等价的当且仅当$\mathrm{Ent}^\sharp(X)=\mathrm{Ent}^\sharp(Y)$，其中$\mathrm{Ent}^\sharp(X)$是$X$的所谓锐熵.这种分类意味着每一个齐次真超度量空间都粗等价于反康托尔集$2^{<ω}$ .为了证明这些结果，我们开发了一种技术的塔，可以有一个独立的利益。
英文摘要：
We prove that two homogeneous ultra-metric spaces $X,Y$ are coarsely equivalent if and only if $\mathrm{Ent}^\sharp(X)=\mathrm{Ent}^\sharp(Y)$ where $\mathrm{Ent}^\sharp(X)$ is the so-called sharp entropy of $X$. This classification implies that each homogeneous proper ultra-metric space is coarsely equivalent to the anti-Cantor set $2^{<ω}$. For the proof of these results we develop a technique of towers which can have an independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
