| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-08-28T09:45:43Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151805 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Herron D. A.: Gromov–Hausdorff distance for pointed metric spaces.J. Anal. 24 (2016), no. 1, 1–38. MR 3755806, 10.1007/s41478-016-0001-x |
| Reference:
|
[5] Ishiki Y.: An interpolation of metrics and spaces of metrics.available at arXiv:2003.13227v1 [math.MG] (2020), 23 pages. |
| Reference:
|
[6] Ishiki Y.: Branching geodesics of the Gromov–Hausdorff distance.Anal. Geom. Metr. Spaces 10 (2022), no. 1, 109–128. MR 4462891, 10.1515/agms-2022-0136 |
| 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. |
| Reference:
|
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| Reference:
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| Reference:
|
[12] Urysohn P.: Beispiel eines nirgends separablen metrischen raumes.Fund. Math. 9 (1927), no. 1, 119–121. 10.4064/fm-9-1-119-121 |
| . |
