Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences

Under \(\mathfrak{p} = \mathfrak{c}\), we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality \({\mathfrak c}\) , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff grou...

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Published inarXiv.org
Main Authors {Matheus Koveroff Bellini, Boero, Ana Carolina, Irene Castro Pereira, de Oliveira Rodrigues, Vinicius, Tomita, Artur Hideyuki
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.10.2018
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Summary:Under \(\mathfrak{p} = \mathfrak{c}\), we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality \({\mathfrak c}\) , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.
ISSN:2331-8422