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