Maximal \delta-separated sets in separable metric spaces and weak forms of choice
Logic
2026-01-14 v1
Abstract
We show that the statement ``In every separable pseudometric space there is a maximal non-strictly \delta-separated set.'' implies the axiom of choice for countable families of sets. This gives answers to a question of Dybowski and G\'{o}rka in [M. Dybowski and P. G\'{o}rka, The axiom of choice in metric measure spaces and maximal \delta-separated sets, Archive for Mathematical Logic 62, 735-749, 2023.]. We also prove several related results.
Keywords
Cite
@article{arxiv.2405.10466,
title = {Maximal \delta-separated sets in separable metric spaces and weak forms of choice},
author = {Michał Dybowski and Przemyslaw Górka and Paul Howard},
journal= {arXiv preprint arXiv:2405.10466},
year = {2026}
}