Definition: Admission topology

The topology ${\tau }_{\Sigma }$ on ${\mathcal{P}}_{\Sigma }$ is the initial locally convex topology for:

1. the coefficient inclusion

   $${\mathcal{P}}_{\Sigma }⟶{\mathcal{T}}_{\mathrm{coeff}};$$

2. every map

   $${\mathsf{b}}_{\Psi ;\mathbf{\eta }}:{\mathcal{P}}_{\Sigma }⟶C^{\infty }(\Sigma ;T^{\ast }M{|}_{\Sigma }).$$

Equivalently, it is the topology induced by the graph embedding into the product of these spaces.