\begin{definition}[Definition:Affine Subspace]
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 $\EE$ {{iff}} 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 $E$.
\end{definition}