Definition:Standard Affine Structure on Vector Space
Let $E$ be a vector space.
Let $\mathcal E$ be the underlying set of $E$.
Let $+$ denote the addition operation $E \times E \to E$, viewed as a mapping $\mathcal E \times E \to \mathcal E$.
Let $-$ denote the subtraction operation $E \times E \to E$, viewed as a mapping $\mathcal E \times \mathcal E \to E$.
Then the set $\mathcal E$, together with the vector space $E$ and the operations $+,-$, is called the standard affine structure on the vector space $E$.