Immersion (mathematics)

For a closed immersion in algebraic geometry, see closed immersion.

In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M → N is an immersion if

is an injective function at every point p of M (where T_pX denotes the tangent space of a manifold X at a point p in X). Equivalently, f is an immersion if its derivative has constant rank equal to the dimension of M: