Exercise 5, Appendix 2

a) Let $G$ be a complete group, such that every neighbourhood of $e$ contains an open subgroup of $G$. For a sequence $(x_n)$ of points of $G$ to be multipliable, it is necessary and sufficient that $\lim_{n \to \infty} x_n = e$.

b) Let $G$ be a complete group, such that every neighbourhood of $e$ contains a distinguished open subgroup of $G$. For a family $(x_i)_{i \in I}$ of points of $G$ to be multipliable, it is necessary and sufficient that $\lim x_i = e$ following the filter of the complements of the finite subsets of $I$ (use IX, p. 126, Exer. 3).