In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly, f : M → N is an immersion if D p f : T p M → T f ( p ) N {\displaystyle D_{p}f:T_{p}M\to T_{f(p)}N\,} is an injective function at every point p of M (where TpX denotes the tangent space of a manifold X at a point p in X and Dp f is the derivative (pushforward) of the map f at point p).
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential pushforward is everywhere injective. Explicitly, f : M → N is an immersion if D p f : T p M → T f ( p ) N {\displaystyle D_{p}f:T_{p}M\to T_{f(p)}N\,} is an injective function at every point p of M (where TpX denotes the tangent space of a manifold X at a point p in X and Dp f is the derivative (pushforward) of the map f at point p).
Source: Wikipedia "Immersion (mathematics)" · CC BY-SA 4.0
Share this article: X · Bluesky