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Embedding of smooth manifolds

  1. Mar 4, 2014 #1
    Consider a smooth map ##F: M \to N## between two smooth manifolds ##M## and ##N##. If the pushforward ##F_*: T_pM \to T_{F(p)} N## is injective and ##F## is a homeomorphism onto ##F(M)## we say that ##F## is a smooth embedding.

    In analogy with a topological embedding being defined as a map that is homemorphic onto it's image I would think that an embedding of smooth manifolds would require that ##F## be a diffeomorphism. So my question is; is the definition above equivalent with ##F## being a diffeomorphism between ##M## and ##N##.
     
  2. jcsd
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