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C^infty question

  1. Nov 13, 2005 #1
    Suppose h and h o f are both C^infty on f(U) and U correspondingly, with U an open set. Assume now that f(U) is open. Is f C^infty on U? Does anyone have a counter example?

    I've edited the question so that it would actually make sense.
    Last edited: Nov 13, 2005
  2. jcsd
  3. Nov 13, 2005 #2


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    trivially false. take h constant.
  4. Nov 13, 2005 #3
    How very stupid of me. Thank you.
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