Metric trees in the Gromov--Hausdorff space
Yoshito Ishiki (2023)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
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.