Let $M$ be a [topological manifold](/page/Topological%20Manifold) with boundary of dimension $n\geq 1$, let $p\in M$, and let $(U,\varphi)$ and $(V,\psi)$ be boundary charts with $p\in U\cap V$, where $\varphi(U)$ and $\psi(V)$ are open subsets of $\mathbb H^n$ in the [subspace topology](/page/Subspace%20Topology). If the last coordinate of $\varphi(p)$ in $\varphi(U)$ satisfies $\varphi(p)_n=0$, then the last coordinate of $\psi(p)$ in $\psi(V)$ satisfies $\psi(p)_n=0$.