# Ambient space

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

## Mathematics

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

- Configuration space
- Manifold and ambient manifold
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
- Differential form

## 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.