Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Continuous Functions
  1. Continuous Function (Replies: 5)

  2. Continuous function? (Replies: 6)

  3. Continuous functions (Replies: 3)

  4. Continuous function (Replies: 8)

Loading...