Definition:Affine Space/Weyl's Axioms

Definition
Let $K$ be a field.

Let $\struct{V, +_V, \circ}$ be a vector space over $K$.

Let $\mathcal E$ be a set on which a mappings are defined:


 * $- : \mathcal E \times \mathcal E \to V$

satisfying the following associativity conditions:

Then the ordered pair $\tuple{\mathcal E, -}$ is an affine space.

Also see

 * Equivalence of Definitions of Affine Space