The tropical charts on ${X^{\rm an}}$ have the following properties:

• (a)

  They form a basis on ${X^{\rm an}}$, i.e. for every open subset $W$ of ${X^{\rm an}}$ and for every $x\in W$, there is a tropical chart $(V,\varphi_{U})$ with $x\in V\subset W$. We may find such a $V$ such that the open subset ${\rm trop}_{U}(V)$ of ${\rm Trop}(U)$ is relatively compact.

• (b)

  The intersection $(V\cap V^{\prime},\varphi_{U\cap U^{\prime}})$ of tropical charts $(V,\varphi_{U})$ and $(V^{\prime},\varphi_{U^{\prime}})$ is a tropical subchart of both.

• (c)

  If $(V,\varphi_{U})$ is a tropical chart and if $U^{\prime\prime}$ is a very affine open subset of $U$ with $V\subset(U^{\prime\prime})^{\rm an}$, then $(V,\varphi_{U^{\prime\prime}})$ is a tropical subchart of $(V,\varphi_{U})$.