在几何学中，一个半空间是用平面分割成两部分的三维欧几里德空间。更一般地说，一个半空间是用一个超平面划分成两部分的仿射空间。也就是说，不属于这个超平面的点被划分成两个凸集（即半空间）。半空间可以开放或封闭。开放的半空间是从仿射空间减去起分割作用的超平面所产生的两个开放集；封闭的半空间是一个开放的半空间与并分割它们的超平面的并集。

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. More generally, a half-space is either of the two parts into which a hyperplane divides an affine space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane.