Ambient space
From Wiki @ Karl Jones dot com
In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object.
Description
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
- Differential form
- Manifold and ambient manifold
- Mathematical object
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
External links
- Ambient space @ Wikipedia.org
