Labeled Trees Generating Separable and Locally Finite Ultrametrics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913884662661120 |
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| author | Dovgoshey, Oleksiy Rovenska, Olga |
| author_facet | Dovgoshey, Oleksiy Rovenska, Olga |
| contents | We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and those that generate locally finite ultrametric spaces. In particular, we establish an analog of König's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Labeled Trees Generating Separable and Locally Finite Ultrametrics Dovgoshey, Oleksiy Rovenska, Olga General Topology 05C63, 05C05, 54E35 We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and those that generate locally finite ultrametric spaces. In particular, we establish an analog of König's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees. |
| title | Labeled Trees Generating Separable and Locally Finite Ultrametrics |
| topic | General Topology 05C63, 05C05, 54E35 |
| url | https://arxiv.org/abs/2506.03853 |