Let $\displaystyle S\subset{R^n} \neq{\emptyset}, x'\in{S}$. Let $\displaystyle C = \left\{{y: y = \lambda (x-x'), \lambda \geq{0}, x\in{S}}\right\}$.

a) Prove that C is a cone and interpretate C geometrically (C is a cone if $\displaystyle \forall{} x\in{C}, \lamba x\in{C}, \lambda \geq{0}$).

b) Suposse S is a close set. ¿Is C necessarely close? If not, ¿what are the conditions for him to be close?

Thank you for every aportation.