An isometric extensor of metrics
Metric Geometry
2024-09-23 v4 General Topology
Abstract
In this paper, for a metrizable space , we consider the space of metrics that generate the same topology of , and that space of metrics is equipped with the supremum metrics. For a metrizable space and a closed subset of it, we construct a map from the space of metrics on into the space of metrics on such that is an extension of metrics and preserves the supremum metrics between metrics.
Cite
@article{arxiv.2407.03030,
title = {An isometric extensor of metrics},
author = {Yoshito Ishiki},
journal= {arXiv preprint arXiv:2407.03030},
year = {2024}
}
Comments
36 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