Ambient space

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


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

Further reading

  • Schilders, W. H. A.; ter Maten, E. J. W.; Ciarlet, Philippe G. (2005). Numerical Methods in Electromagnetics. Special Volume. Elsevier. pp. 120ff. ISBN 0-444-51375-2.
  • Wiggins, Stephen (1992). Chaotic Transport in Dynamical Systems. Berlin: Springer. pp. 209ff. ISBN 3-540-97522-5.
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