grandes-ecoles 2023 Q3

grandes-ecoles · France · x-ens-maths-b__mp Proof Proof That a Map Has a Specific Property

Let $r \in \mathbb { R } _ { + } ^ { * }$ such that $r \leqslant \rho$. Show that the map $\mathscr { D } _ { \rho } ( \mathbb { R } ) \rightarrow \mathscr { D } _ { r } ( \mathbb { R } )$ which associates to a function $f$ its restriction to $U _ { r }$ is injective.

Let $r \in \mathbb { R } _ { + } ^ { * }$ such that $r \leqslant \rho$. Show that the map $\mathscr { D } _ { \rho } ( \mathbb { R } ) \rightarrow \mathscr { D } _ { r } ( \mathbb { R } )$ which associates to a function $f$ its restriction to $U _ { r }$ is injective.

Paper Questions

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