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arXiv · 2103.12917

Countably compact group topologies on arbitrarily large free Abelian groups

M. K. Bellini·K. P. Hart·V. O. Rodrigues·A. H. Tomita
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Abstract

We prove that if there are $\mathfrak c$ incomparable selective ultrafilters then, for every infinite cardinal $\kappa$ such that $\kappa^\omega=\kappa$, there exists a group topology on the free Abelian group of cardinality $\kappa$ 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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BibTeXRIS

M. K. Bellini, K. P. Hart, V. O. Rodrigues, A. H. Tomita. 2021-03-24. Countably compact group topologies on arbitrarily large free Abelian groups. https://arxiv.org/abs/2103.12917

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