Affine set

A set $$C$$ is called an affine set if any affine combination of the points in the set belongs to the set. Affine combination is just a linear combination where the coefficients of the combination sum to one.

Affine sets are "very big", i.e., they have to be infinite. For example, they are lines, planes, subspaces, cubes, hyperplanes etc. (see Section 2.2 ).