Definition:Half-Plane/Open/Lower

Definition
Let $\PP$ be a Cartesian plane.

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

The open lower half-plane $\HH_{\text {OL} }$ is the area of $\PP$ below $\LL$.

That is, where $y < 0$:


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

Also see

 * Definition:Open Upper 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