The homomorphism of inclusion of $k$-algebras $V(L)\rightarrow\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi)$ induces a continuous map between topological spaces $\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi))\rightarrow(\spec V(L))^{\mathrm{an}}$ which is closed. Moreover, the map is injective.