Continuity at the named levels

For a closed cone $\Gamma \subset {\dot{T}}^{\ast }X$, use the normal topology on ${{\mathcal{D}}^{\prime }}_{\Gamma }(X)$: the strong distribution seminorms

and the Fourier seminorms

For compact $K\subset M^n$, set

Finite species components and graded symmetry carry their induced topologies.

The normal-topology facts used here are hypocontinuity of tensor products and compatible distribution products, continuity of transversal pullback and support-proper pushforward, and hypocontinuity of smooth multiplication BDH. Fixing one factor gives a continuous linear map. Constant-coefficient differentiation is continuous, as follows from