Definition:Embedding (Differential Geometry)
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Definition
Let $m,n\geq1$ be natural numbers.
Let $U\subset\R^n$ be open.
Let $f : U \to \R^m$ be a mapping.
Then $f$ is a $C^k$-embedding if and only if $f$ is:
- injective
- a $C^k$-immersion
- a homeomorphism on its image
Rank
The rank of an embedding is the rank of its differential at any point.
Smooth Embedding
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