Set ${\mathcal{X}}={\mathbb{D}}^{2}$ and $D=E_{0}+E_{1}$ the union of the coordinate axes, with coordinates $(z_{0},z_{1})$. Then ${\mathcal{U}}={\mathcal{X}}$ is itself an adapted coordinate chart. In these coordinates, $\operatorname{Log}_{{\mathcal{U}}}\colon{\mathcal{U}}\setminus D\to\sigma_{\mathcal{U}}$ becomes the map $({\mathbb{D}}^{*})^{2}\to[0,1]$ sending $(z_{0},z_{1})$ to $\log|z_{1}|/\log|z_{0}z_{1}|$. As a consequence, given $t\in{\mathbb{R}}_{+}^{*}$ and $0<\varepsilon\ll 1$, the closure in ${\mathcal{X}}^{\mathrm{hyb}}$ of the closed subset

$$F_{\varepsilon}:=\{0<|z_{0}|,|z_{1}|\leq\varepsilon,|z_{0}|^{t+\varepsilon}\leq|z_{1}|\leq|z_{0}|^{t-\varepsilon}\}\subset{\mathbb{D}}^{2}$$

is given by ${\bar{F}}_{\varepsilon}=F_{\varepsilon}\cup I_{\varepsilon}$, where $I_{\varepsilon}:=\{t\in[0,1]\mid\frac{t-\varepsilon}{1+t-\varepsilon}\leq t\leq\frac{t+\varepsilon}{1+t+\varepsilon}\}$. Further, the sets ${\bar{F}}_{\varepsilon}$, for $0<\varepsilon\ll 1$ form a basis of closed neighborhoods of the point $\frac{t}{1+t}\in[0,1]$ in ${\mathcal{X}}^{\mathrm{hyb}}$. See Figure 1.