Let E {\displaystyle {}E} be an affine space over the K {\displaystyle {}K} -vector space V {\displaystyle {}V} . A subset F ⊆ E {\displaystyle {}F\subseteq E} is called an affine subspace, if ( F {\displaystyle {}F} is empty or)
with a point P ∈ E {\displaystyle {}P\in E} and a K {\displaystyle {}K} -linear subspace U ⊆ V {\displaystyle {}U\subseteq V} .
