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