Katsuhisa Koshino

activity

20152026

most citedThe topological classification of spaces of metrics with the uniform convergence topology

1 citations · 1 across the 13 of their papers we have counts for

collaborators

15 papers

math.FA2026

Isometries between the unit spheres of spaces of metrics

Katsuhisa Koshino

Given a topological space $Z$ , let $P M (Z)$ be the space of bounded continuous pseudometrics on $Z$ , which is endowed with the sup-norm, and let $S P M (Z)$ be the unit sphere of $PM(Z…

math.FA2026

Banach-Stone type theorems on uniformly continuous and lipschitz continuous pseudometrics

Katsuhisa Koshino

In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.

math.FA2026

Compactness of averaging operators on non-reflexive Lebesgue spaces

Katsuhisa Koshino

Let $X$ be a Borel and Borel-regular metric measure space whose closed balls are of positive and finite measure. In this paper, we shall give equivalent conditions for averaging op…

math.FA2025

Isometries between spaces of metrics

Katsuhisa Koshino

Given a metrizable space $Z$ , denote by $PM (Z)$ the space of continuous bounded pseudometrics on $Z$ , and denote by $AM (Z)$ the one of continuous bounded admissible met…

math.MG2024

On isometric universality of spaces of metrics

Yoshito Ishiki, Katsuhisa Koshino

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 met…

math.GN2024

On the Borel complexity and the complete metrizability of spaces of metrics

Katsuhisa Koshino

Given a metrizable space $X$ , let $A M (X)$ be the space of continuous bounded admissible metrics on $X$ , which is endowed with the sup-metric. In this paper, we shall investigate th…

math.FA2024

Compactness of averaging operators on Banach function spaces

Katsuhisa Koshino

Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging oper…

math.GN2022

Characterizing compact sets in $L^{p}$ -spaces and its application

Katsuhisa Koshino

In this paper, we give a characterization of compact sets in $L^{p}$ -spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion,…

math.GN2022

The topological type of spaces consisting of certain metrics on locally compact metrizable spaces with the compact-open topology

Katsuhisa Koshino

For a separable locally compact but not compact metrizable space $X$ , let $α X = X \cup {x_{\infty}}$ be the one-point compactification with the point at infinity $x_{\infty}$ . We den…

math.GN2021★ 1 cited

The topological classification of spaces of metrics with the uniform convergence topology

Katsuhisa Koshino

For a metrizable space $X$ of density $κ$ , let $P M (X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its top…

math.FA2020

The space consisting of uniformly continuous functions on a metric measure space with the $L^{p}$ norm

Katsuhisa Koshino

In this paper, we shall show that the space of real-valued uniformly continuous functions on a metric measure space with the $L^{p}$ norm is homeomorphic to the subspace consisting o…

math.GN2019

Characterizations of topological manifolds modeled on absorbing sets in non-separable Hilbert spaces and the discrete cells property

Katsuhisa Koshino

In this paper, we characterize infinite-dimensional manifolds modeled on absorbing sets in non-separable Hilbert spaces by using the discrete cells property, which is a general pos…

math.GN2015

Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

Katsuhisa Koshino

Let $Fin (X)$ be the hyperspace consisting of non-empty finite subsets of a space $X$ endowed with the Vietoris topology. In this paper, we characterize a metrizable space $X$ …

math.GN2015

On a hyperspace of compact subsets which is homeomorphic to a non-separable Hilbert space

Katsuhisa Koshino

Let $X$ be a metrizable space and $Comp (X)$ be the hyperspace consisting of non-empty compact subsets of $X$ endowed with the Vietoris topology. In this paper, we give a nece…

math.GN2015

The compact strong Z-set property in a hyperspace of finite subsets

Katsuhisa Koshino

Let X be a non-degenerate, connected, locally path-connected metrizable space and Fin(X) be the hyperspace consisting of non-empty finite subsets in X endowed with the Vietoris top…

Isometries between the unit spheres of spaces of metrics

Banach-Stone type theorems on uniformly continuous and lipschitz continuous pseudometrics

Compactness of averaging operators on non-reflexive Lebesgue spaces

Isometries between spaces of metrics

On isometric universality of spaces of metrics

On the Borel complexity and the complete metrizability of spaces of metrics

Compactness of averaging operators on Banach function spaces

Characterizing compact sets in Lp-spaces and its application

The topological type of spaces consisting of certain metrics on locally compact metrizable spaces with the compact-open topology

The topological classification of spaces of metrics with the uniform convergence topology

The space consisting of uniformly continuous functions on a metric measure space with the Lp norm

Characterizations of topological manifolds modeled on absorbing sets in non-separable Hilbert spaces and the discrete cells property

Topological structures of hyperspaces of finite sets in non-separable metrizable spaces

On a hyperspace of compact subsets which is homeomorphic to a non-separable Hilbert space

The compact strong Z-set property in a hyperspace of finite subsets

Characterizing compact sets in $L^{p}$ -spaces and its application

The space consisting of uniformly continuous functions on a metric measure space with the $L^{p}$ norm