Definition:Affine Subspace

Definition
Let $\mathcal E$ be an affine space with difference space $E$.

Let $\mathcal F \subseteq \mathcal E$ be a subset of $\mathcal E$.

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


 * $\displaystyle F_p := \left\{{ q - p : q \in \mathcal F }\right\}$

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

Also see

 * Affine Subspace is Affine Space