Type: Article

Countably compact groups without non-trivial convergent sequences

Hrusak, M., van Mill, J., Ramos-García, A., Shelah, S.;

Abstract:

We construct, in ZFC, a countably compact subgroup of 2c 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 G0 and G1 such that the product G0 × G1 is not countably compact, thus answering a classical problem of Comfort.