Work

Spaces of metrics are Baire

Year: 2025

Type: article

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. As an application, we prove that typical metrics take typical reals.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2025.109408

Author: Yoshito Ishiki

Institution: Tokyo Metropolitan University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funders: Japan Society for the Promotion of Science, RIKEN