Upper half-plane

In mathematics, the upper half-plane, ${\displaystyle \,{\mathcal {H}}\,}$, is the set of points ${\displaystyle (x,y)}$ in the Cartesian plane with ${\displaystyle y>0}$. The lower half-plane is defined similarly, by requiring that ${\displaystyle y}$ be negative instead. Each is an example of two-dimensional half-space.