Geodesic
Metric trees in the Gromov--Hausdorff space
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 73-82.

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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.
DOI : 10.14712/1213-7243.2023.012
Classification : 51F99, 53C23
Keywords: metric tree; Gromov--Hausdorff distance 
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Ishiki, Yoshito. Metric trees in the Gromov--Hausdorff space. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 73-82. doi : 10.14712/1213-7243.2023.012. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.012/

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