IEVref: 102-03-02 ID: Language: en Status: Standard Term: point space Synonym1: affine space Synonym2: Synonym3: Symbol: Definition: for a given vector space, set of elements called points, for which an element ${U}_{\text{AB}}$ of the vector space is associated to any ordered pair of points A and B with the following properties: for any two points A and B, ${U}_{\text{BA}}=-\text{\hspace{0.17em}}{U}_{\text{AB}}$, 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 1 to entry: 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. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: