Countably compact groups from a selective ultrafilter

Garcia-Ferreira, S.; Tomita, A.; Watson, S.

doi:10.1090/S0002-9939-04-07684-1

Countably compact groups from a selective ultrafilter
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by S. Garcia-Ferreira, A. H. Tomita and S. Watson

Proc. Amer. Math. Soc. 133 (2005), 937-943

DOI: https://doi.org/10.1090/S0002-9939-04-07684-1

Published electronically: September 29, 2004

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Abstract:

We prove that the existence of a selective ultrafilter on $\omega$ implies the existence of a countably compact group without non-trivial convergent sequences all of whose powers are countably compact. Hence, by using a selective ultrafilter on $\omega$, it is possible to construct two countably compact groups without non-trivial convergent sequences whose product is not countably compact.

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