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Products of Embedded Submanifolds

  1. Oct 24, 2013 #1
    I'm trying to come up with a simple proof that if [itex]M[/itex] is an embedded submanifold of [itex]N[/itex], and [itex]P[/itex] is an embedded submanifold of [itex]Q[/itex], then [itex]M×P[/itex] is an embedded submanifold of [itex]N×Q[/itex]. I'm thinking this could be easily done using showing that [itex]M×P[/itex] satisfies the local [itex]k[/itex]-slice condition, or that the product of smooth embeddings (from the respective inclusion maps) is also a smooth embedding.
  2. jcsd
  3. Oct 24, 2013 #2
    Yes, both the slice-condition as the map-condition work. But what did you try? Where are you stuck?
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