3 problems

Topology conjecture. Any proper dp-minimal expansion of $(\mathbb{Z},+)$ which eliminates $\exists^\infty$ defines a non-discrete group topology on $(\mathbb{Z},+)$.

Let $G$ be a group, and let $\mathfrak{c}$ denote the cardinality of the continuum. A subgroup of $G$ is unconditionally closed if it is closed in every Hausdorff group topology on…

Let $G$ be an acylindrically hyperbolic group with no non-trivial finite normal subgroups. A group topology on $G$ is topologically simple if its only closed normal subgroups are t…