Consider the hyperplane, {x in R^n: a'x = b} (where a is in R^n\{0}). This partitions R^n into two ( closed) half spaces: {x: a'x = b} and {x: a'x = b}. The two associated open halfspaces are {x: a'x b} and {x: a'x b}.

A mathematical model used to approximate the earth when performing some calculations in seismology. The model is much simpler than the real earth.