The set of distances in a Polish metric space

2025/08/31 by John D. Clemens, Clemens, John D.
Mathematics · #03E15 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2509.01027

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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