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

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Boero A., Tomita A.

Fundamenta Mathematicae

2011

tom 212

nr 3

235-260

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Boero A.

1 Tomita A.

1 2011

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