Concerning the convergence of a series in a topological group, it is said in this post (Infinite sum of elements in a finite field) :
"You need the topology so you can talk about convergence of sequences. You need addition to be continuous with respect to this topology so that you can talk about convergence of infinite series."
A series converge if the sequence of partial sum converge. Then, the convergence of a series amounts to the convergence of a sequence.
Question : Why must we have this additional hypothesis on the continuity of addition, to make sense of the convergence of a series?
