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IEVref: | 102-03-02 | ID: | |

Language: | en | Status: Standard | |

Term: | point space | ||

Synonym1: | affine space | ||

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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
, there is a unique point P such that ${U}_{\text{OP}}=r$*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: | |||

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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: | |||

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Domain5: |

- 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
, there is a unique point P such that ${U}_{\text{OP}}=r$*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.