Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Ishiki, Yoshito"'
Autor:
Ishiki, Yoshito, Koshino, Katsuhisa
A metric space $(M, d)$ is said to be universal for a class of metric spaces if all metric spaces in the class can be isometrically embedded into $(M, d)$. In this paper, for a metrizable space $Z$ possessing abundant subspaces, we first prove that t
Externí odkaz:
http://arxiv.org/abs/2409.17701
Autor:
Ishiki, Yoshito
In this paper, for a metrizable space $Z$, we consider the space of metrics that generate the same topology of $Z$, and that space of metrics is equipped with the supremum metrics. For a metrizable space $X$ and a closed subset $A$ of it, we construc
Externí odkaz:
http://arxiv.org/abs/2407.03030
Autor:
Ishiki, Yoshito
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. In this paper, for every metrizable space, we establish that the space
Externí odkaz:
http://arxiv.org/abs/2402.04565
Autor:
Ishiki, Yoshito
In 1959, Arens and Eells proved that every metric space can be isometrically embedded into a real linear space as a closed subset. In later years, Michael pointed out that every metric space can be isometrically embedded into a real linear space as a
Externí odkaz:
http://arxiv.org/abs/2309.06704
Autor:
Ishiki, Yoshito
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 gives a characterization of the Urysohn universal ultrametric spaces.
Externí odkaz:
http://arxiv.org/abs/2303.17471
Autor:
Ishiki, Yoshito
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 recently investigated an ultrametric analogue of this space. The isometr
Externí odkaz:
http://arxiv.org/abs/2302.00306
Autor:
Ishiki, Yoshito
We first prove that for every metrizable space $X$, for every closed subset $F$ whose complement is zero-dimensional, the space $X$ can be embedded into a product space of the closed subset $F$ and a metrizable zero-dimensional space as a closed subs
Externí odkaz:
http://arxiv.org/abs/2212.13409
Autor:
Ishiki, Yoshito
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 metric if and only if it is zero-dimensional. In this paper, we shall devel
Externí odkaz:
http://arxiv.org/abs/2210.02170
Autor:
Ishiki, Yoshito
Publikováno v:
Topology and its Applications. (2022) No. 108387
We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we prove an extension theorem of proper metrics, wh
Externí odkaz:
http://arxiv.org/abs/2207.12905
Autor:
Ishiki, Yoshito
Publikováno v:
Topology and its Applications vol.327 (2023), 108442
For a metrizable space $X$, we denote by $\mathrm{Met}(X)$ the space of all metric that generate the same topology of $X$. The space $\mathrm{Met}(X)$ is equipped with the supremum distance. In this paper, for every strongly zero-dimensional metrizab
Externí odkaz:
http://arxiv.org/abs/2207.12765