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Thread: help me solve this problem please..

  1. December 13th 2009, 10:14 PM #1
    felixmcgrady
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    help me solve this problem please..

    f: R to R. For all open subset U of R, we have f(U) is open, too.


    Prove that: f is monotonic.
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  2. December 14th 2009, 09:28 AM #2
    redsoxfan325
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    Quote Originally Posted by felixmcgrady View Post
    f: R to R. For all open subset U of R, we have f(U) is open, too.


    Prove that: f is monotonic.
    If f is not monotonic, it will have a local extremum at some point x_0. What can you say about an open ball around f(x_0)?
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