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

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8 papers · 1 filter

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.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.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…

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

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

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