A subset \(S\subset M\) endowed with the subspace topology and a smooth atlas is called embedded submanifold if the embedding \(S\hookrightarrow M\) is an injective immersion which is a homeomorphism onto its image. The manifold \(M\) is often called ambient manifold of \(S\).
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Related Definitions Link to heading
- codimension
- smooth functions on embedded submanifolds
- tangent space of an embedded submanifold
- Riemannian submanifold