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## Injective Immersion Vs Embedding

Differential Geometry
Tsakanikas Nickos
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### Injective Immersion Vs Embedding

• Show that a closed, injective, continuous map is a (topological) embedding.
• Give an example to show that an injective immersion can fail to be an embedding.
• Show that an injective immersion $F \ \colon M \longrightarrow N$ (between smooth manifolds) is a (smooth) embedding if either $M$ is compact or $F$ is a proper map.