Affine space/Subspace/Definition

Let ${\displaystyle {}E}$ be an affine space over the ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$. A subset ${\displaystyle {}F\subseteq E}$ is called an affine subspace, if (${\displaystyle {}F}$ is empty or)

${\displaystyle {}F=P+U\,}$

with a point ${\displaystyle {}P\in E}$ and a ${\displaystyle {}K}$-linear subspace ${\displaystyle {}U\subseteq V}$.