Exercise 3.F.26

Proof. Let $U$ be the subspace of $V$ such that

We have that

v ∈ V : v ∈⋂ φ∈Γ null ⁡ φ

=

v ∈ V : v ∈ null ⁡ φ for every φ ∈ Γ

=

v ∈ V : φ(v) = 0 for every φ ∈ Γ

By Exercise 25, $\Gamma =U^0$. Therefore

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