2407.03030Jul 3, 202436 pages. I have fixed gaps on topologies of Wasserstein spaces on arbitrary metric spaces. I have also provided a general observation on topologies on spaces of measurable functions using Lusin's theorem

An isometric extensor of metrics

Yoshito Ishiki

Metric Geometry General Topology

arXiv PDF

Abstract

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 construct a map $E$ from the space of metrics on $A$

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into the space of metrics on

X

such that

E

is an extension of metrics and preserves the supremum metrics between metrics.

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