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arXiv · 2405.10466

Maximal \delta-separated sets in separable metric spaces and weak forms of choice

Michał Dybowski·Przemyslaw Górka·Paul Howard
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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.

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Michał Dybowski, Przemyslaw Górka, Paul Howard. 2024-05-16. Maximal \delta-separated sets in separable metric spaces and weak forms of choice. https://doi.org/10.1017/jsl.2025.10176

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