Corollary: The forbidden admission hypothesis is genuinely dropped

The identity sending a mixed kernel to its actual polynomial functional is not sequentially continuous from the normal stage of Lemma lem:normal into $({\mathcal{P}}_{\Sigma },{\tau }_{\Sigma })$ at $b_f$.

Thus the present admission maps do not satisfy the combination:

Proof. Lemma lem:normal gives the convergence in the source topology. Theorem thm:IX1 excludes the convergence of its images.