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-\v{C}ech 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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拓扑群的舒尔超滤波器和玻尔致密化
本文研究了群上的舒尔超滤波器。利用离散群的 Stone-\v{C}ech 压缩的代数结构和舒尔超滤波器,我们给出了拓扑群的玻尔压缩的新描述。通过这种方法,我们可以描述作为拓扑群的图群的特征。也就是说,只有当且仅当 $G$ 上的每个舒尔超滤波器都收敛于 $G$ 的单位时,图群 $G$ 才是拓扑群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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