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Keywords:
metric tree; Gromov--Hausdorff distance
metric tree; Gromov--Hausdorff distance
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.
References:
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