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

Ana Carolina Boero; Artur Hideyuki Tomita

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

Similarity:

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...