1
Soit \(E = {\cal B}(\N,\R) = \{ \text{suites } u = (u_n) \text{ born{é}es}\}\). On munit \(E\) de la norme : \(\|u\| = \sum_{n=0}^\infty \frac{|u_n|}{2^n}\). Montrer que \(A = \{u\in E \text{ tq } \forall\ n\in\N,\ 0\le u_n\le 1\}\) est compact.
Soit \(E = {\cal B}(\N,\R) = \{ \text{suites } u = (u_n) \text{ born{é}es}\}\). On munit \(E\) de la norme : \(\|u\| = \sum_{n=0}^\infty \frac{|u_n|}{2^n}\). Montrer que \(A = \{u\in E \text{ tq } \forall\ n\in\N,\ 0\le u_n\le 1\}\) est compact.