AI 中文总结
研究不可数局部有限群的端点问题，采用通过希格森冠拓扑结构的粗几何方法，借助子群不变性解释粗开闭集边界，利用相关技术实现几何刚性，得出此类群恰好有一个端点的结论。
AI 中文摘要
D. F. Holt的一个经典结果表明，不可数局部有限离散群恰好有一个端点。传统方法依赖上同调方法和几乎不变子集的组合操作，而本文通过粗几何，借助希格森冠的拓扑结构来建立该结果。通过根据子群不变性解释粗开闭集的边界，在群的大规模几何上评估其相关特征函数。利用斯科伦包提取和周期性粗重路由技术，强制实现禁止多个端点的几何刚性。
英文摘要
It is a classical result of D. F. Holt that an uncountable, locally finite discrete group possesses exactly one end. While traditional approaches rely on cohomological methods and the combinatorial manipulation of almost-invariant subsets, we establish this result through coarse geometry via the topological structure of the Higson corona. By interpreting the boundaries of coarsely clopen sets in terms of subgroup invariance, we evaluate their associated characteristic functions on the large-scale geometry of the group. Utilizing a Skolem-hull extraction and a periodic coarse rerouting technique, we force a geometric rigidity that prohibits multiple ends.
