Half-space (geometry)

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.

[1] If the space is two-dimensional, then a half-space is called a half-plane (open or closed).

[2][3] A half-space in a one-dimensional space is called a half-line[4] or ray.

More generally, a half-space is either of the two parts into which a hyperplane divides an n-dimensional space.

The open (closed) lower half-space is defined similarly, by requiring that xn be negative (non-positive).