Definition:Half-Plane/Closed/Lower

Definition
Let $\PP$ be a Cartesian plane.

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

The closed lower half-plane $\HH_{\text {CL} }$ is the area of $\PP$ below and including $\LL$.

That is, where $y \le 0$:


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

Also see

 * Definition:Closed Upper Half-Plane


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


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


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