The topology actually supplied

For a fixed local module, the inherited coefficient seminorms can be written

These are the usual compact-set smooth seminorms named by XIV-I. The source also states continuity of its reconstruction into ${\mathcal{D}}^{\prime }(V)$.

If a topology on the local image is required, this patch adopts the quotient-topology convention

This convention pushes the named coefficient topology to the image. It is not attributed to a separately stated source definition of the topology of the complete ${\mathcal{K}}_{\mathrm{int}}$.

No assertion is made that this quotient topology equals the subspace topology inherited from ${\mathcal{D}}^{\prime }(V)$. No global Fréchet structure, choice of representatives, or continuous right inverse is introduced. A topology for the common graph image still requires its full presentation and gluing conventions.