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Let $V$ be an $n$ dimensional vector space, let $R$ be a finite set of vectors.

  1. Will there exist a hyperplane which does not contain any of the vectros from $R$?

  2. How to construct such a hyperplane?

  3. 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.

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    What field is $V$ over?2012-10-05
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    By hyperplane do you mean an affine space or a subspace?2012-10-05

2 Answers 2