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arXiv · 2608.12494

Countable uniformly discrete sets in functionally balanced groups

Dekui Peng·Li-Hong Xie·Jiang Yang
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Abstract

We prove that every countable left uniformly discrete subset of a Hausdorff functionally balanced topological group is right thin. As applications, we answer two questions of Bouziad and Troallic: every left precompact subset of a Hausdorff functionally balanced group is right precompact, and every Hausdorff $\omega$-narrow functionally balanced group is a SIN group.

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Dekui Peng, Li-Hong Xie, Jiang Yang. 2026-08-12. Countable uniformly discrete sets in functionally balanced groups. https://arxiv.org/abs/2608.12494

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