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Metric trees in the Gromov--Hausdorff space (2112.05345v1)
Published 10 Dec 2021 in math.MG
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.