arXiv:2405.10466 Abstract | arXiv Analytics

arXiv:2405.10466 [math.LO]Abstract References Reviews Resources

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

Michał Dybowski, Przemyslaw Górka, Paul Howard

Published 2024-05-16Version 1

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.

Categories: math.LO

Subjects: 03E25, 03E35, 30L99

Keywords: separable metric spaces, weak forms, metric measure spaces, separable pseudometric space, countable families

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