The set of distances in a Polish metric space
Logic
2025-09-03 v1
Abstract
We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets.
Cite
@article{arxiv.2509.01027,
title = {The set of distances in a Polish metric space},
author = {John D. Clemens},
journal= {arXiv preprint arXiv:2509.01027},
year = {2025}
}