Proposition 2

Let A and B be commutative complex Banach algebras. For every algebra morphism $\pi : A\rightarrow B$, the mapping $\mathsf{X}'(\pi )$ is a proper partial mapping of $\mathsf{X}(B)$ into $\mathsf{X}(A)$.

In fact, $\mathsf{X}'(\pi )$ is a continuous mapping of $\mathsf{X}'(B)$ into $\mathsf{X}'(A)$ (I, p. 10). The point at infinity of $\mathsf{X}'(B)$ (resp. of $\mathsf{X}'(A)$) is the null character, and one has $\mathsf{X}'(\pi )(0) = 0$.