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Limits of an approach

  1. Feb 24, 2014 #1


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    I have seen (in H Cartan's differential calculus) a proof that if F is a Banch space, L(E,F) where E is some vector space, is also a Banach space. One of the main points of the proof is based on the behaviour of a function being "proper" (continuous) on a ball of arbitrary radius "n" and by such being able to extend the property to the entire space.

    I was wondering when/how does this type of argument fail?
  2. jcsd
  3. Feb 24, 2014 #2


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    Notation question. What is L(E,F)?
  4. Feb 24, 2014 #3


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    I apologize, it is the space of linear functions from E to F.
  5. Feb 27, 2014 #4


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    Mustn't E also be a normed space? How can one otherwise talk about a ball with a certain radius in E?
  6. Feb 27, 2014 #5


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    yes, but not necessarily complete.
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