Definition:Standard Affine Structure on Vector Space

Definition
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 $E$.

Also see

 * Vector Space with Standard Affine Structure is Affine Space