grandes-ecoles 2022 Q17

grandes-ecoles · France · x-ens-maths__psi_cpge Proof Proof of Equivalence or Logical Relationship Between Conditions
Let $E$ be a non-empty subset of $\mathbb{R}^d$. With $E^+$ and $E^{++}$ as defined in question 16, show that $E = E^{++}$ if and only if $E$ is a closed convex cone.
Let $E$ be a non-empty subset of $\mathbb{R}^d$. With $E^+$ and $E^{++}$ as defined in question 16, show that $E = E^{++}$ if and only if $E$ is a closed convex cone.