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Continuous Functions

  1. Apr 13, 2005 #1
    Cb is set of all complex valued bounded functions
    R is set of Real numbers

    Define F:Cb(R)->Cb(R) by F(f)=f^2 for all 'points' f is an element of Cb(R). Prove that F is continuous.

    Can someone give me some guidance on how to get started with this one?
  2. jcsd
  3. Apr 13, 2005 #2


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    You should probably go straight back to the definition of a limit... but first you need to figure out the space you're working over. What sort of topology does Cb(R) have?
    Last edited: Apr 13, 2005
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