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تسجيل مستخدم جديدCountably compact group topologies on arbitrarily large free Abelian groups
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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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