On a question of Dikranjan and Zava

Abstract

Let $G$ be a non-discrete countable metrizable abelian topological group endowed with the coarse structure $\mathcal{C}$ generated by compact subsets of $G$. We prove that $asdim(G,\mathcal{C})=\infty$. For an infinite cyclic subgroup $G$ of the circle, this answers a question of Dikranjan and Zava [3].

arXiv admin note: text overlap with arXiv:1903.04915