What are the differences between an embedding and a diffeomorphism? Examples and extreme cases would be great.
2026-04-01 21:29:09.1775078949
Embedding and diffeomorphisms
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An embedding is a diffeomorphism onto its image, so the only difference between an embedding and a diffeomorphism is that an embedding may not be surjective, that is all.
For example, $(s,t)\mapsto (s\cos(t),s\sin(t),t)$ is an embedding of $\mathbb{R}^2$ onto $\mathbb{R}^3$ but not a diffeomorphism.