arXiv subjects

Matheus Koveroff Bellini

Publications and source records attributed to Matheus Koveroff Bellini.

3 recordsLinked to original sources

arXiv2022

$\mathcal{U}$-compact group topologies without convergent sequences on countably cofinal torsion-free Abelian groups

We obtain a forcing construction that shows that it is consistent that the torsion-free Abelian group $\mathbb{Q}^{(λ)}$ admits a Hausdorff group topology which is also $\mathcal{U}$-compact and contains no non-trivial convergent sequences, where $λ$ is a cardinal whose cofinality is $ω$ and $\mathcal{U}$ is a selective ultrafilter. This answers a question posed in arXiv:1904.05928.

math.GN↗

arXiv2020

Forcing a classification of non-torsion Abelian groups of size at most $2^\mathfrak c$ with non-trivial convergent sequences

We force a classification of all the Abelian groups of cardinality at most $2^\mathfrak c$ that admit a countably compact group with a non-trivial convergent sequence. In particular, we answer (consistently) Question 24 of Dikranjan and Shakhmatov for cardinality at most $2^{\mathfrak c}$, by showing that if a non-torsion Abelian group of size at most $2^\mathfrak c$ admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.

math.GN↗

arXiv2019

On $p$-compact group topologies on direct sums of ${\mathbb Q}$

We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(κ)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $κ=κ^ω$. In particular, this gives the first arbitrarily large examples of countably compact groups without non-trivial convergent sequences that are torsion-free.

math.GN↗