AFFINE SET

Affine set (or affine manifold, affine variety, linear variety, flat.) One that contains the line through any two of its points; i.e., x, y in S implies ax + (1-a)y is in S for all real values, a. The dimension of an affine set is that of the (unique) subspace parallel to it. Dimensions of 0, 1 and 2 are called points, lines and planes, resp.