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arXiv · 2409.07280

Schur ultrafilters and Bohr compactifications of topological groups

Serhii Bardyla·Pavol Zlatoš
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Abstract

In this paper we investigate Schur ultrafilters on groups. Using the algebraic structure of Stone-Čech compactifications of discrete groups and Schur ultrafilters, we give a new description of Bohr compactifications of topological groups. This approach allows us to characterize chart groups that are topological groups. Namely, a chart group $G$ is a topological group if and only if each Schur ultrafilter on $G$ converges to the unit of $G$.

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Serhii Bardyla, Pavol Zlatoš. 2025-03-28. Schur ultrafilters and Bohr compactifications of topological groups. https://arxiv.org/abs/2409.07280

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