If $\mathcal{P}(\phi)$ is continous, then for any $\epsilon>0$, one has

$$\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi))\subseteq\text{Int}^{\mathrm{top}}_{V_{{\scriptscriptstyle\bullet}}}(\mathfrak{M}(\widehat{V}_{{\scriptscriptstyle\bullet}}(L,\phi(\epsilon)))),$$

where $\text{Int}^{\mathrm{top}}_{V_{{\scriptscriptstyle\bullet}}}$ denotes the topological interior as subspace of $\spec(V_{{\scriptscriptstyle\bullet}}(L))^{\mathrm{an}}$.