Definition:Half-Plane/Open/Upper

Definition
Let $\PP$ be a Cartesian plane.

Let $\LL$ be the $x$-axis.

The open upper half-plane $\HH_{\text {OU} }$ is the area of $\PP$ above $\LL$.

That is, where $y > 0$:


 * $\HH_{\text {OU} } := \set {\tuple {x, y}: y \in \R_{> 0} }$

Also see

 * Definition:Open Lower Half-Plane


 * Definition:Open Right Half-Plane
 * Definition:Open Left Half-Plane


 * Definition:Closed Upper Half-Plane
 * Definition:Closed Lower Half-Plane


 * Definition:Closed Left Half-Plane
 * Definition:Closed Right Half-Plane