Remark

If $G$ is a commutative topological group, written additively, then the mapping $(x, y) \to x + y$ of $G \times G$ onto $G$ is a strict morphism. For since $(x + x') + (y + y') = (x + y) + (x' + y')$ it is a homomorphism of $G \times G$ onto $G$; also it is continuous, and the image of a neighbourhood $V \times V$ of the origin in $G \times G$ under this mapping is the neighbourhood $V + V$ of the origin in $G$.