immersion
Let and be manifolds, and let be a mapping . Choose , and let . Recall that is the derivative of at , and is the tangent space of manifold at point .
If is injective, then is said to be an immersion at x. If is an immersion at every point, it is called an immersion.
If the image of is also closed, then is called a closed immersion.
The notion of closed immersion (http://planetmath.org/ClosedImmersion) for schemes is the analog of this notion in algebraic geometry.
Title | immersion |
---|---|
Canonical name | Immersion |
Date of creation | 2013-03-22 12:35:04 |
Last modified on | 2013-03-22 12:35:04 |
Owner | bshanks (153) |
Last modified by | bshanks (153) |
Numerical id | 8 |
Author | bshanks (153) |
Entry type | Definition |
Classification | msc 57R42 |
Related topic | Submersion |
Defines | closed immersion |