A COUNTABLY COMPACT GROUP TOPOLOGY ON ABELIAN ALMOST TORSION-FREE GROUPS FROM SELECTIVE ULTRAFILTERS

Assuming the existence of c incomparable selective ultrafilters, we show that the real line and the unit circle group can be endowed with a countably compact Hausdorff group topology without non-trivial convergent sequences, answering a question proposed by Madariaga-Garcia and Tomita [10]. More generally, we prove that this result remains valid for every abelian almost torsion-free group of cardinality c. We also show, under the same assumption, that every abelian almost torsion-free topological group of countable weight and cardinality c admits a Hausdorff group topology which is T-1-independent of the original one. So, the MA-constructions presented by Tkachenko and Yaschenko [13] can be obtained under weaker set-theoretic assumptions than MA for countable posets.