Exercise 10, § 5

Let E₁, E₂ and F be three topological vector spaces, G₁ (resp. G₂) an everywhere dense subspace of E₁ (resp. E₂), and S₁ (resp. S₂) a family of bounded subsets of G₁ (resp. G₂). Let H be a set of separately continuous bilinear mappings from E₁ × E₂ into F; if the set of restrictions to G₁ × G₂ of the mappings u ∈ H is (S₁, S₂)-equihypocontinuous, then so is H.