grandes-ecoles 2021 Q1.1

grandes-ecoles · France · x-ens-maths__pc Proof Proof of Set Membership, Containment, or Structural Property

Let $K$ be a closed, bounded and infinite subset of $\mathbb{C}$. Show that $\|P\|_K$ belongs to $\mathbb{R}$ for all $P \in \mathbb{C}[X]$.

Let $K$ be a closed, bounded and infinite subset of $\mathbb{C}$. Show that $\|P\|_K$ belongs to $\mathbb{R}$ for all $P \in \mathbb{C}[X]$.