4 citations · 17 across the 18 of their papers we have counts for
5 papers · 1 filter
Metric trees in the Gromov--Hausdorff space
Yoshito Ishiki
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 th…
Continua in the Gromov--Hausdorff space
Yoshito Ishiki
We first prove that for all compact metrizable spaces, there exists a topological embedding of the compact metrizable space into each of the sets of compact metric spaces which are…
Fractal dimensions in the Gromov--Hausdorff space
Yoshito Ishiki
In this paper, we first show that for all four non-negative real numbers, there exists a Cantor ultrametric space whose Hausdorff dimension, packing dimension, upper box dimension,…
Branching geodesics of the Gromov--Hausdorff distance
Yoshito Ishiki
In this paper, we first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of a…
On dense subsets in spaces of metrics
Yoshito Ishiki
In spaces of metrics, we investigate topological distributions of the doubling property, the uniform disconnectedness, and the uniform perfectness, which are the quasi-symmetricall…