2021/12/10 by Ishiki, Yoshito
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2112.05345
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.