Countably compact groups without non-trivial convergent sequences

Hrušák, M.; van Mill, J.; Ramos-García, U.; Shelah, S.

doi:10.1090/tran/8222

Countably compact groups without non-trivial convergent sequences
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by M. Hrušák, J. van Mill, U. A. Ramos-García and S. Shelah PDF

Trans. Amer. Math. Soc. 374 (2021), 1277-1296 Request permission

Abstract:

We construct, in 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.

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