Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.21763 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929444848926720 |
|---|---|
| author | Bellaïche, Itamar |
| author_facet | Bellaïche, Itamar |
| contents | This paper demonstrates that every ultrametric space is homeomorphic to a clade space of a pruned tree, i.e., a subspace of a tree's canopy. Furthermore, it characterizes several topological properties of ultrametrizable spaces through the features of their representing trees. This approach suggests that topological properties of ultrametrizable spaces should be studies via the study of naturally ordered pruned trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ultrametrizable spaces are homeomorphic to clade spaces of pruned trees Bellaïche, Itamar General Topology This paper demonstrates that every ultrametric space is homeomorphic to a clade space of a pruned tree, i.e., a subspace of a tree's canopy. Furthermore, it characterizes several topological properties of ultrametrizable spaces through the features of their representing trees. This approach suggests that topological properties of ultrametrizable spaces should be studies via the study of naturally ordered pruned trees. |
| title | Ultrametrizable spaces are homeomorphic to clade spaces of pruned trees |
| topic | General Topology |
| url | https://arxiv.org/abs/2407.21763 |