Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Lebedeva, Nina, Petrunin, Anton
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214077901