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• Euclidean space
  A '''Euclidean space''' or, more precisely, a '''Euclidean''' '''''n'''''-'''space''' == Euclidean space ==
  9 KB (1,403 words) - 02:22, 14 October 2013
• Euclidean space/Definition
  122 bytes (14 words) - 04:50, 2 September 2009
• Euclidean space/Related Articles
  338 bytes (42 words) - 19:08, 5 October 2009

Page text matches

• Banach space/Related Articles
  {{r|Euclidean space}}
  423 bytes (60 words) - 15:14, 28 July 2009
• Normed space
  #The Euclidean space <math>\mathbb{R}^n</math> endowed with the Euclidean norm <math>\|x\|=\sqrt
  982 bytes (148 words) - 07:17, 3 December 2007
• Vector field/Definition
  A vector function on the three-dimensional [[Euclidean space]] <font style="vertical-align: 9.2%"> <math>\scriptstyle \mathbb{E}^3</math
  182 bytes (20 words) - 04:04, 31 October 2008
• Norm (mathematics)/Definition
  ...vector space that generalises the notion of the distance from a point of a Euclidean space to the origin.
  157 bytes (26 words) - 15:01, 4 January 2009
• Dot product/Definition
  A type of [[vector]] multiplication in [[Euclidean space]]s which produces a [[scalar]] result.
  131 bytes (17 words) - 13:46, 7 July 2008
• Topological space/Definition
  A mathematical structure (generalizing some aspects of Euclidean space) defined by a family of open sets.
  141 bytes (19 words) - 17:39, 17 June 2009
• Rigid motion
  ...'' is a transformation which preserves the geometrical properties of the [[Euclidean space]]. Since Euclidean properties may be defined in terms of [[distance]], the ...of rigid motions are the ''translations'' or displacements. If we regard Euclidean space of ''n'' dimensions as an [[affine space]] built on a [[real number|real]]
  3 KB (392 words) - 14:42, 28 November 2008
• Geometry
  ...ry)|plane]], a higher dimensional Euclidean space, a sphere or other [[non-Euclidean space]], or more generally, a [[manifold]].
  2 KB (232 words) - 03:09, 8 March 2024
• Inner product space
  #The [[Euclidean space]] <math>\mathbb{R}^n</math> endowed with the real inner product <math>\lang
  1 KB (204 words) - 14:38, 4 January 2009
• Heine–Borel theorem/Definition
  In Euclidean space of finite dimension with the usual topology, a subset is compact if and onl
  160 bytes (26 words) - 05:33, 29 December 2008
• Banach space
  ...dimensional normed space is a Banach space (due to its isomorphism to some Euclidean space).
  2 KB (317 words) - 13:13, 14 July 2008
• Euclid's Elements/Related Articles
  {{r|Euclidean space}}
  313 bytes (48 words) - 14:58, 7 December 2008
• Complete metric space
  * The real numbers '''R''', and more generally finite-dimensional [[Euclidean space]]s, with the usual metric are complete.
  3 KB (441 words) - 12:23, 4 January 2009
• Norm (mathematics)
  ...generalizes to vector spaces the notion of the distance from a point of a Euclidean space to the origin.
  880 bytes (157 words) - 22:28, 20 February 2010
• Heine–Borel theorem
  A Euclidean space of fixed finite dimension ''n'' also forms a [[metric space]] with the Eucl
  2 KB (381 words) - 08:54, 29 December 2008
• Hilbert space/Related Articles
  {{r|Euclidean space}}
  955 bytes (150 words) - 15:15, 28 July 2009
• Compact space
  ...he set is a subset of a finite dimensional [[normed space]], such as the [[Euclidean space]]s, then compactness is equivalent to that set being closed and [[bounded s * The ''[[Heine-Borel theorem]]'': In [[Euclidean space]] with the usual topology, a [[subset]] is compact if and only if it is clo
  4 KB (652 words) - 14:44, 30 December 2008
• Euclidean space
  A '''Euclidean space''' or, more precisely, a '''Euclidean''' '''''n'''''-'''space''' == Euclidean space ==
  9 KB (1,403 words) - 02:22, 14 October 2013
• Parallel (geometry)
  ...ce". (This is different, of course, if, more generally (hyper-)planes in [[Euclidean space|higher-dimensional]] spaces are considered.)
  5 KB (852 words) - 05:23, 17 April 2010
• Bounded set
  The [[Heine–Borel theorem]] states that a subset of the [[Euclidean space]] '''R'''^''n'' is [[compact space|compact]] if and only if it is
  1 KB (188 words) - 05:37, 29 December 2008