Definition:Affine Subspace

Definition
Let $\EE$ be an affine space with tangent space $E$.

Let $\FF \subseteq \EE$ be a subset of $\EE$.

Then $\FF$ is an affine subspace of $\mathcal E$ there exists a point $p \in \EE$ such that:


 * $F_p := \set {q - p: q \in \FF}$

is a vector subspace of the vector space $E$.

Also known as
Some sources give this as affine manifold.

Also see

 * Affine Subspace is Affine Space