Metric trees in the Gromov--Hausdorff space
Metric Geometry
2021-12-13 v1
Abstract
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 its all non-empty open subsets have infinite topological dimension.
Keywords
Cite
@article{arxiv.2112.05345,
title = {Metric trees in the Gromov--Hausdorff space},
author = {Yoshito Ishiki},
journal= {arXiv preprint arXiv:2112.05345},
year = {2021}
}
Comments
9 pages. This paper is strongly rerated to my papers arXiv:2110.01881 and arXiv:2111.08199. There are some overlapped explanation and definitions