• for any two points A and B, $U_{\text{BA}}=-U_{\text{AB}}$,
• for any three points A, B and C, $U_{\text{AB}}+U_{\text{BC}}=U_{\text{AC}}$,
• for a given point O and a given vector r, there is a unique point P such that $U_{\text{OP}}=r$

NOTE A point space and the associated vector space have the same dimension. The point space derived from the three-dimensional Euclidean vector space is a model of the usual geometrical three-dimensional space.