论文标题
无数非平凡融合序列的紧凑型组
Countably compact groups without non-trivial convergent sequences
论文作者
论文摘要
我们在$ \ mathsf {zfc} $中构造了一个$ 2^{\ mathfrak {c}} $的$ 2^{\ mathfrak {c}} $的亚组，而没有非平凡的收敛序列，回答了van douwen的旧问题。结果，我们还证明了两个非常紧凑的组$ \ mathbb {g} _ {0} $和$ \ mathbb {g} _ {1} $，使得产品$ \ mathbb {g} _ {0} _ {0} \ times \ times \ mathbb {g}
We construct, in $\mathsf{ZFC}$, a countably compact subgroup of $2^{\mathfrak{c}}$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb{G}_{0}$ and $\mathbb{G}_{1}$ such that the product $\mathbb{G}_{0} \times \mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.
