In analogy with differential geometry on manifolds, we set $C^{\infty}(V):=A^{0,0}(V)$ for any open subset $V$ of ${X^{\rm an}}$ and a smooth function on $V$ is just a differential form of bidegree $(0,0)$. Since tropicalization maps are continuous, it is clear that a smooth function is a continuous function on $V$. By the Stone-Weierstrass theorem, the space $C_{c}^{\infty}(V)$ of smooth functions with compact support in $V$ is a dense subalgebra of $C_{c}(V)$ (see [CD12], Proposition 3.3.5).