We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{ \tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{ \tau})$. If $G$ is discrete then $(G, S_{ \tau})$ is a finitary coarse group studding in Geometric Group Theory. The main result: if a topological abelian group $(G, \tau)$ contains a non-trivial converging sequence then $asdim \ (G, S_{ \tau})= \infty $.
Categories: math.GN
