Definition 3

Let Λ be a set and V a subset of $\mathbf{C}^{\Lambda}$. One says that V is polynomially convex if V is the set of points $(c_{\lambda})_{\lambda\in\Lambda}$ of $\mathbf{C}^{\Lambda}$ such that

$|P((c_{\lambda}))|\leqslant$ sup$_{c\in V}|P(c)|$

for every $P\in \mathbf{C}[(X_{\lambda})]$.