From the 1 of 10 linked papers with an AI index.
10 papers
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…
Algebraic structures on non-Archimedean Urysohn universal metric spaces
Yoshito Ishiki
The paper studies how valued-field structures, including p‑adic and Levi‑Civita fields, can be placed on Urysohn universal ultrametric spaces, showing that many such spaces are iso…
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…
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 factorization of metric spaces
Yoshito Ishiki
We first prove that for every metrizable space , for every closed subset whose complement is zero-dimensional, the space can be embedded into a product space of the clos…
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…