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

Preferred term

Euclidean space  

Definition(s)

  • Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Euclidean_space)

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RDF/XML TURTLE JSON-LD Last modified 8/31/23