Let H be a hyperplane in a linear space that is not a subspace. Then there is

Question:

Let H be a hyperplane in a linear space that is not a subspace. Then there is a unique linear functional f ∊ X' such that
H = {x ∊ X: f (x) = 1}
On the other hand, where H is a subspace, we have the following primitive form of the Hahn-Banach theorem (section 3.9.1).