Spaces of metrics are Baire
Metric Geometry
2024-06-04 v3
Abstract
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 of metrics on the metrizable space is Baire. We also show that the set of all complete metrics is comeager in the space of metrics. Moreover, we investigate non--Archimedean analogues of these results.
Cite
@article{arxiv.2402.04565,
title = {Spaces of metrics are Baire},
author = {Yoshito Ishiki},
journal= {arXiv preprint arXiv:2402.04565},
year = {2024}
}
Comments
13 pages