Displaying similar documents to “A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact”

The existence of initially ω 1 -compact group topologies on free Abelian groups is independent of ZFC

Artur Hideyuki Tomita (1998)

Commentationes Mathematicae Universitatis Carolinae

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It was known that free Abelian groups do not admit a Hausdorff compact group topology. Tkachenko showed in 1990 that, under CH, a free Abelian group of size ℭ admits a Hausdorff countably compact group topology. We show that no Hausdorff group topology on a free Abelian group makes its ω -th power countably compact. In particular, a free Abelian group does not admit a Hausdorff p -compact nor a sequentially compact group topology. Under CH, we show that a free Abelian group does not admit...

On the Stieltjes moment problem on semigroups

Torben Maack Bisgaard (2002)

Czechoslovak Mathematical Journal

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We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).