任意大自由阿尔贝群上的可数紧群拓扑
Countably compact group topologies on arbitrarily large free Abelian groups
摘要：
证明了：如果存在$\mathfrak c$的不可比较的选择超滤子，则对任意无限基数$κ$，使得$κ^ω=κ$，在基数为$κ$的自由阿尔贝群上存在群拓扑，不存在非平凡的收敛序列，并且使得任意有限幂是可数紧的.特别地，存在任意大的可数紧群。这回答了1992年D. Dikranjan和D.沙赫马托夫
英文摘要：
We prove that if there are $\mathfrak c$ incomparable selective ultrafilters then, for every infinite cardinal $κ$ such that $κ^ω=κ$, there exists a group topology on the free Abelian group of cardinality $κ$ without nontrivial convergent sequences and such that every finite power is countably compact. In particular, there are arbitrarily large countably compact groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.
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