A half-space in 
-dimensional Euclidean space
is a region on one side of an 
-dimensional hyperplane.
An open half-space excludes the bounding hyperplane,
while a closed half-space includes it. For example, an open half-space in three dimensions is 
, 
, 
, while an open half-plane
is given by the two-dimensional region
satisfying 
,
.
