Difference between revisions of "Ambient space"
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| − | In [[mathematics]], especially in geometry and topology, an ambient space is the space surrounding a mathematical object. | + | In [[mathematics]], especially in [[geometry]] and [[topology]], an '''ambient space''' is the space surrounding a [[mathematical object]]. |
== Description == | == Description == | ||
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* [[Configuration space]] | * [[Configuration space]] | ||
* [[Manifold and ambient manifold]] | * [[Manifold and ambient manifold]] | ||
| + | * [[Mathematical object]] | ||
* [[Submanifolds and Hypersurfaces]] | * [[Submanifolds and Hypersurfaces]] | ||
* [[Riemannian manifolds]] | * [[Riemannian manifolds]] | ||
Revision as of 12:27, 16 September 2016
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
- Manifold and ambient manifold
- Mathematical object
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
- Differential form
External links
- Ambient space @ Wikipedia.org
