Delhomme-Laflamme-Pouzet-Sauer space as groupoid
| Autor: | Dovgoshey, Oleksiy, Kostikov, Alexander |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathbb{R}^{+}=[0, \infty)$ and let $d^+$ be the ultrametric on $\mathbb{R}^+$ such that $d^+ (x,y) = \max\{x,y\}$ for all different $x,y \in \mathbb{R}^+$. It is shown that the monomorphisms of the groupoid $(\mathbb{R}^+, d^+)$ coincide with the injective ultrametric-preserving functions and that the automorphisms of $(\mathbb{R}^+, d^+)$ coincide with the self-homeomorphisms of $\mathbb{R}^+$. The structure of endomorphisms of $(\mathbb{R}^+, d^+)$ is also described. Comment: 16 pages |
| Databáze: | arXiv |
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