Let $Z=\spec(A_{Z})$ be an affine $k$-variety, $\vvvert\mathord{\cdot}\vvvert$ an algebra norm on $A_{Z}$ and $\mathcal{A}_{Z}$ be the $k$-Banach algebra obtained by completing $A_{Z}$ with respect to $\vvvert\mathord{\cdot}\vvvert$. Then the canonical homomorphism of $k$-algebras from $A_{Z}$ to $\mathcal{A}_{Z}$ induces a continuous map which embeds the Berkovich spectrum $\mathfrak{M}(\mathcal{A}_{Z})$ into $Z^{an}$ as a compact subspace (and is closed since $Z^{\mathrm{an}}$ is Hausdorff), and the Berkovich topology coincides with the induced topology from $Z^{an}$.