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arXiv · 1810.05140

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

{Matheus Koveroff Bellini·Ana Carolina Boero·Irene Castro Pereira·Vinicius de Oliveira Rodrigues·Artur Hideyuki Tomita
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Abstract

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.

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{Matheus Koveroff Bellini, Ana Carolina Boero, Irene Castro Pereira, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita. 2018-10-11. Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences. https://arxiv.org/abs/1810.05140

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