AI 中文总结
本文分类了全集合齐次测地空间，指出除经典例子外还包括有限价数的万有度量树。
AI 中文摘要
如果一个度量空间的任意子集之间的等距映射都能扩展为整个空间的等距映射，则该度量空间被称为全集合齐次的。我们对全集合齐次测地空间进行了分类；除经典例子外，它们还包括有限价数的万有度量树。
英文摘要
A metric space is called all-set-homogeneous if every isometry between two of its subsets extends to an isometry of the whole space. We classify all-set-homogeneous geodesic spaces: besides the classical examples, they include the universal metric trees of finite valence. We also prove that every complete all-set-homogeneous length space is geodesic, and hence the same classification holds in this setting.
Comments12 pages, 7 figures
