Exercise 22, § 3

Soit Ω une compact subset of $\mathbf{C}^n$. The mapping

is a homeomorphism of Ω onto a polynomially convex compact subset of $\mathbf{C}^{2n}$. (Let $A =\mathscr{C}(\Omega ),z_i$ be the coordinate functions on $\mathbf{C}^n$. Then $(z_i|\Omega , z_i|\Omega )_{1\leqslant i\leqslant n}$ is a topological generator system of A, and the mapping considered is the mapping from $\mathsf{X}(A) = \Omega$ into $\mathbf{C}^{2n}$ defined by this topological generator system.)