A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

CAPES (Brazil)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq (Brazil)[308467/2007-8]