Delhomme-Laflamme-Pouzet-Sauer space as groupoid
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913409843331072 |
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| author | Dovgoshey, Oleksiy Kostikov, Alexander |
| author_facet | Dovgoshey, Oleksiy Kostikov, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Delhomme-Laflamme-Pouzet-Sauer space as groupoid Dovgoshey, Oleksiy Kostikov, Alexander General Topology Primary 26A30, Secondary 54E35, 20M20 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. |
| title | Delhomme-Laflamme-Pouzet-Sauer space as groupoid |
| topic | General Topology Primary 26A30, Secondary 54E35, 20M20 |
| url | https://arxiv.org/abs/2407.00508 |