4 citations · 24 across the 23 of their papers we have counts for
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Algebraically independent distances and rigid metrics
Yoshito Ishiki
We study metrics whose distances on distinct two-point subsets are algebraically independent over the rationals. We prove that every compatible metric on a strongly zero-dimensiona…
The topology of Gromov--Hausdorff space
Yoshito Ishiki
We prove that the space of isometry classes of nonempty compact metric spaces, equipped with the Gromov--Hausdorff distance, is homeomorphic to the real separable infinite-dimensio…
A counterexample to Scottish Book Problem 155
Yoshito Ishiki
We construct real Banach spaces and and a bijection which preserves all pairwise distances on every closed ball of radius but is not a global isometr…
Borelness of Moduli Spaces of Metrics Implies Separability
Yoshito Ishiki, Tomoki Uda
Let X be a metrizable space, and let Met(X) denote the space of metrics compatible with the topology of X, regarded as a subspace of the space of continuous pseudometrics with the…
Absolute Borel Complexity of Moduli Spaces of Ultrametrics
Yoshito Ishiki
Let be an ultrametrizable space. We study the space of bounded compatible ultrametrics on , equipped with its natural non-Archimedean distance. For every positive integer le…
Algebraic structures on non-Archimedean Urysohn universal metric spaces
Yoshito Ishiki
We investigate valued-field structures on Urysohn universal ultrametric spaces. We introduce -adic Levi--Civita fields as subfields of -adic Hahn fields and treat them togeth…