Let $V$ be an $n$ dimensional vector space, let $R$ be a finite set of vectors.
Will there exist a hyperplane which does not contain any of the vectros from $R$?
How to construct such a hyperplane?
Do I need the vectors linearly indepenedent?
I need to prove this result to show the existance of weyl chambers. I understand that there will be such hyperplane as baire category theorem says a complete metric space can not be union of no where dense sets.