Topology

On each fixed-support, bounded-polynomial-degree stage, give ${\mathcal{P}}_{\Sigma ,\min }$ the locally convex topology generated by:

1. the strong distribution seminorms of its symmetric coefficient kernels;

2. every scalar pairing

   $$F⟼⟨{\mathsf{ch}}_{\Phi }(D_{{\chi }_1}\cdots D_{{\chi }_r}F),\zeta ⟩,$$

   for fixed smooth directions ${\chi }_j$, fixed smooth configuration $\Phi$, and compact spatial boundary test $\zeta$.

Assemble the stages by the locally convex inductive-limit topology. Denote it by ${\tau }_{\mathrm{bd}}$.