1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Analysis: Continuous open mappings.

  1. Jul 5, 2008 #1
    Here is a mystifying question from Rudin Chapter 4, #15

    Call a mapping of X into Y "open" if f(V) is an open set in Y whenever V is an open set in X. Prove that every continuous open mapping of Reals into the Reals is monotonic.​

    I'm having trouble proving this, in part, because I don't even think it's true. Wouldn't say... [tex]f(x)= x^{2}[/tex] map open sets to open sets? And [tex]f(x)= x^{2}[/tex] isn't monotonic on the Reals. Can someone tell me why [tex]f(x)= x^{2}[/tex] isn't a continuous open mapping of Reals into the Reals that is NOT monotonic.
     
    Last edited: Jul 5, 2008
  2. jcsd
  3. Jul 5, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    What is f((-1,1))?
     
  4. Jul 5, 2008 #3
    [0, 1)

    THANKS. Got it now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Analysis: Continuous open mappings.
  1. Open map (Replies: 2)

  2. Open mappings (Replies: 3)

  3. Continuous map (Replies: 25)

Loading...