Article
| Title: | Metric trees in the Gromov--Hausdorff space (English) |
| Author: | Ishiki, Yoshito |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 73-82 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension. (English) |
| Keyword: | metric tree |
| Keyword: | Gromov--Hausdorff distance |
| MSC: | 51F99 |
| MSC: | 53C23 |
| idZBL: | Zbl 07790583 |
| idMR: | MR4631791 |
| DOI: | 10.14712/1213-7243.2023.012 |
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| Date available: | 2023-08-28T09:45:43Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151805 |
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| Reference: | [7] Ishiki Y.: Continua in the Gromov–Hausdorff space.Topology Appl. 312 (2022), Paper No. 108058, 10 pages. MR 4387932, 10.1016/j.topol.2022.108058 |
| Reference: | [8] Ishiki Y.: Fractal dimensions in the Gromov–Hausdorff space.available at arXiv: 2110.01881v5 [math.MG] (2022), 24 pages. MR 4387932 |
| Reference: | [9] Jansen D.: Notes on pointed Gromov–Hausdorff convergence.available at arXiv: 1703.09595v1 [math.MG] (2017), 48 pages. |
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