路连通局部唯一测地度量空间与Sup度量乘积的等距可约性
Isometries of Products of Path-Connected Locally Uniquely Geodesic Metric Spaces with the Sup Metric are Reducible
摘要：
设$M_i$和$N_i$是非点的路径连通局部唯一测地度量空间，$f:\prod_{i=1}^m M_i\to \prod_{i=1}^n N_i$是等距空间，其中$\prod_{i=1}^n N_i$和$\prod_{i=1}^m M_i$被赋予超度量.然后，对于所有$i$，$m=n$和重新索引后的$M_i$与$N_i$等距。此外，$f$是重新索引因子空间的等距和等距$f_i:M_i\to N_i$的乘积的等距的组合。
英文摘要：
Let $M_i$ and $N_i$ be path-connected locally uniquely geodesic metric spaces that are not points and $f:\prod_{i=1}^m M_i\to \prod_{i=1}^n N_i$ be an isometry where $\prod_{i=1}^n N_i$ and $\prod_{i=1}^m M_i$ are given the sup metric. Then $m=n$ and after reindexing $M_i$ is isometric to $N_i$ for all $i$. Moreover $f$ is a composition of an isometry that reindexes the factor spaces and an isometry that is a product of isometries $f_i:M_i\to N_i$.
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。
