Injective Immersion Vs Embedding

Differential Geometry
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Tsakanikas Nickos
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Injective Immersion Vs Embedding

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Post by Tsakanikas Nickos »

  • 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.
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