4 citations · 24 across the 23 of their papers we have counts for
24 papers · 1 filter
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…
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…
On isometric universality of spaces of metrics
Yoshito Ishiki, Katsuhisa Koshino
A metric space is said to be universal for a class of metric spaces if all metric spaces in the class can be isometrically embedded into . In this paper, for a met…
An isometric extensor of metrics
Yoshito Ishiki
In this paper, for a metrizable space , we consider the space of metrics that generate the same topology of , and that space of metrics is equipped with the supremum metrics.…
Spaces of metrics are Baire
Yoshito Ishiki
For a metrizable space, we consider the space of all metrics generating the same topology of the metrizable space, and this space of metrics is equipped with the supremum metric. I…
A non-Archimedean Arens--Eells isometric embedding theorem on valued fields
Yoshito Ishiki
In 1959, Arens and Eells proved that every metric space can be isometrically embedded into a normed linear space as a closed subset. In later years, in the paper on a short proof o…
Characterizations of Urysohn universal ultrametric spaces
Yoshito Ishiki
In this paper, using the existence of infinite equidistant subsets of closed balls, we characterize the injectivity of ultrametric spaces for finite ultrametric spaces, which also…
Constructions of Urysohn universal ultrametric spaces
Yoshito Ishiki
In this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric subspace of the space of all continuous func…
Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces
Yoshito Ishiki
Urysohn constructed a separable complete universal metric space homogeneous for all finite subspaces, which is today called the Urysohn universal metric space. Some authors have re…
Strongly rigid metrics in spaces of metrics
Yoshito Ishiki
A metric space is said to be strongly rigid if no positive distance is taken twice by the metric. In 1972, Janos proved that a separable metrizable space has a strongly rigid metri…
Simultaneous extensions of metrics and ultrametrics of high power
Yoshito Ishiki
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric sp…
Extending proper metrics
Yoshito Ishiki
We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on -compact locally compact Hausdorff spaces. As its…
On comeager sets of metrics whose ranges are disconnected
Yoshito Ishiki
For a metrizable space , we denote by the space of all metric that generate the same topology of . The space is equipped with the supremum…
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…
An embedding, an extension, and an interpolation of ultrametrics
Yoshito Ishiki
The notion of the ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces.…
An interpolation of metrics and spaces of metrics
Yoshito Ishiki
As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an appl…
A characterization of metric subspaces of full Assouad dimension
Yoshito Ishiki
We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces a…
On the Assouad dimension and convergence of metric spaces
Yoshito Ishiki
We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric…
Quasi-symmetric invariant properties of Cantor metric spaces
Yoshito Ishiki
For metric spaces, the doubling property, the uniform disconnectedness, and the uniform perfectness are known as quasi-symmetric invariant properties. The David-Semmes uniformizati…