## Yoshito Ishiki

*Metric trees in the Gromov-Hausdorff space*

Comment.Math.Univ.Carolin. 64,1 (2023) 73-82.**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 all its nonempty open subsets have infinite topological dimension.

**Keywords:** metric tree; Gromov-Hausdorff distance

**DOI:** DOI 10.14712/1213-7243.2023.012

**AMS Subject Classification:** 53C23 51F99

PDF