Let $n\in\mathbb{N}$. In the \reftext{def:euclidean-space-rn-2026a}{Euclidean space} $\mathbb{R}^n$, the closed upper half-space is the subset

A subset $\Omega\subseteq H^n$ is said to be open in $H^n$ if there exists an \reftext{def:open-subset-euclidean-space-2026a}{open subset} $U\subseteq\mathbb{R}^n$ such that

The boundary hyperplane of $H^n$ is the subset

The interior of $H^n$ is the subset