Ambient space

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An ambient space or ambient configuration space is the space surrounding an object.

Mathematics[edit]

Three examples of different geometries: Euclidean, elliptical, and hyperbolic geometry

In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object. For example, a line may be studied in isolation, or it may be studied as an object in two-dimensional space — in which case the ambient space is the plane, or as an object in three-dimensional space — in which case the ambient space is three-dimensional. To see why this makes a difference, consider the statement "Lines that never meet are necessarily parallel." This is true if the ambient space is two-dimensional, but false if the ambient space is three-dimensional, because in the latter case the lines could be skew lines, rather than parallel.

See also[edit]

Further reading[edit]

  • W H A Schilders, E.J .W. ter Maten, Philippe G. Ciarlet, Numerical Methods in Electromagnetics: Special Volume, Elsevier 2005. (ed., with particular attention to page 120+.)
  • Stephen Wiggins, Chaotic Transport in Dynamical Systems. 1992. (ed., with particular attention to page 209+.)
  • "Relative Hyperbolicity, Trees of Spaces and Cannon–Thurston Maps" arXiv:0708.3578, 2007
  • "Relative Hyperbolic Extensions of Groups and Cannon–Thurston Maps" arXiv:0801.0933, 2008