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... > topology > algebraic topology > manifold > differentiable manifold > Lie group > homogeneous space > affine space
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... > geometry > topological space > manifold > differentiable manifold > Lie group > homogeneous space > affine space
... > geometry > differential geometry > differentiable manifold > Lie group > homogeneous space > affine space
... > topology > differential topology > differentiable manifold > Lie group > homogeneous space > affine space
... > algebra > group theory > topological group > Lie group > homogeneous space > affine space
algebra > abstract algebra > algebraic structure > homogeneous space > affine space
geometry > affine geometry > affine space

Preferred term

affine space  

Definition

  • In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead displacement vectors, also called translation vectors or simply translations, between two points of the space. Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. Likewise, it makes sense to add a displacement vector to a point of an affine space, resulting in a new point translated from the starting point by that vector.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Affine_space)

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http://data.loterre.fr/ark:/67375/PSR-XZ1PX8C3-D

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Exactly matching concepts

https://en.wikipedia.org/wiki/Affine_space
en.wikipedia.org
https://fr.wikipedia.org/wiki/Espace_affine
fr.wikipedia.org