Half-Spaces

Definition: Upper Half-Spaces

The $n$-dimensional closed upper-half space is the subset of ${\mathbb{R}}^n$ defined as

$$\left\{\left[\begin{array}{c}{v}_1\\ ⋮\\ v_n\end{array}\right]\in {\mathbb{R}}^n|v_n\ge 0\right\}$$

and equipped with the Euclidean topology.

NOTATION

$${\mathbb{H}}^n$$