Affine subspace/Affine generating system/Definition

Let ${\displaystyle {}E}$ be an affine space over the ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$, and let ${\displaystyle {}F\subseteq E}$ be an affine subspace. A family of points ${\displaystyle {}P_{i}\in F}$, ${\displaystyle {}i\in I}$, is called an affine generating system of ${\displaystyle {}F}$, if ${\displaystyle {}F}$ is the smallest affine subspace of ${\displaystyle {}E}$ containing all points ${\displaystyle {}P_{i}}$.