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arXiv · 2112.05345

Metric trees in the Gromov--Hausdorff space

Yoshito Ishiki
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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.

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Yoshito Ishiki. 2021-12-10. Metric trees in the Gromov--Hausdorff space. https://arxiv.org/abs/2112.05345

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