Schur ultrafilters and Bohr compactifications of topological groups

2024/09/11 by Bardyla, Serhii, Zlatoš, Pavol
#FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2409.07280

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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