无穷可数阿贝尔群上的极小几乎周期群拓扑：Comfort问题的一个解
Minimally almost periodic group topology on infinite countable Abelian groups: A solution to Comfort's question
摘要：
对于无界阿贝尔群$G$的任意可数子群$H$，存在完备Hausdorff群拓扑$τ$使得$H$是$(G,τ)$的冯诺依曼根。特别地，我们得到了Comfort问题的肯定答案：任何无界可数阿贝尔群都有一个完备的Hausdorff极小概周期（MinAP）群拓扑.有界无限阿贝尔群允许MinAP群拓扑当且仅当它的所有前导Ulm-Kaplansky不变量都是无限的。此外，如果$G$是可数无限的，则可以选择MinAP组拓扑是完整的。
英文摘要：
For any countable subgroup $H$ of an unbounded Abelian group $G$ there is a complete Hausdorff group topology $τ$ such that $H$ is the von Neumann radical of $(G,τ)$. In particular, we obtain the positive answer to Comfort's question: any unbounded countable Abelian group admits a complete Hausdorff minimally almost periodic (MinAP) group topology. A bounded infinite Abelian group admits a MinAP group topology if and only if all its leading Ulm-Kaplansky invariants are infinite. If, in addition, $G$ is countably infinite, a MinAP group topology can be chosen to be complete.
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