Let X and Y be manifoldsMathworldPlanetmath, and let f be a mapping f:XY. Choose xX, and let y=f(x). Recall that dfx:Tx(X)Ty(Y) is the derivative of f at x, and Tz(Z) is the tangent space of manifold Z at point z.

If dfx is injective, then f is said to be an immersion at x. If f is an immersion at every point, it is called an immersion.

If the image of f is also closed, then f is called a closed immersion.

The notion of closed immersion ( for schemes is the analog of this notion in algebraic geometryMathworldPlanetmathPlanetmathPlanetmath.

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 SubmersionMathworldPlanetmath
Defines closed immersion