$ on $\mathsf{U}_{\hbox{\tiny $\mathrm{rec}$}}\mathbb{A}$ satisfy properties (0) and (0) of definition \[lam\] for the local homeomorphism $\amalg$.  *Property* (0): Let $g_0, g_0$ be two points in $\mathsf{U}_{\hbox{\tiny $\mathrm{rec}$}}\mathbb{H}$, $h_0, h_0$ be two points in the intersection $\mathcal{U}_{g_0} \cap$ $\mathcal{U}_{g_0}$ and $p^{+,0}$ be the projection from $\mathcal{U}_{g^-}\times\mathcal{U}_{g^+}\times\mathbb{R}$ onto $\mathcal{U}_{g^+}