Definition:Diffeomorphism on Image

Open Set in $\R^n$

Let $n$ and $k$ be natural numbers.

Let $U \subset \R^n$ be an open set.

Let $f : U \to \R^n$ be a mapping.

Then $f$ is a $C^k$-diffeomorphism on its image if and only if $\map f U$ is open and $f : U \to f \sqbrk U$ is a $C^k$-diffeomorphism.

Differentiable Manifold

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