Countably compact group topologies on arbitrarily large free Abelian groups
Matheus K. Bellini (Universidade de São Paulo)
Klaas Pieter Hart (TU Delft - Analysis)
Vinicius O. Rodrigues (Universidade de São Paulo, York University)
Artur H. Tomita (Universidade de São Paulo)
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Abstract
We prove that if there are c incomparable selective ultrafilters then, for every infinite cardinal κ such that κω=κ, there exists a group topology on the free Abelian group of cardinality κ 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.