Gromov-Hausdorff Geometry of Metric Trees
| Autor: | Ivanov, A. O., Mikhailov, I. N., Tuzhilin, A. A. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study metric trees, without any finiteness restrictions. For subsets of such trees, a condition that guarantees that the Hausdorff and Gromov--Hausdorff distances from the subset to the entire metric tree are the same is obtained. This result allows to construct a new class of shortest geodesics (in the proper class of all metric spaces) connecting such subset of a metric tree with the tree itself. In particular, the technique elaborated is demonstrated on subsets of the real line. Comment: 10 pages, 0 figures |
| Databáze: | arXiv |
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