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Question on continuity

  1. Aug 4, 2009 #1
    I´ve been trying to solve this for some time: Let f: R to R be an increasing on a dense set. Define g(x)=inf_{x<t in D} f(t). Show that continuity of f does not imply continuity of g but uniform continuity of f does imply uniform continuity of g.
    Any help?
     
  2. jcsd
  3. Aug 4, 2009 #2

    berkeman

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    Staff: Mentor

    Is this homework/coursework? If not, what is the application?
     
  4. Aug 4, 2009 #3
    I encounter this question while studying Probability by my own. It's not homework/coursework. The application is understanding properties of distribution functions.
     
  5. Aug 4, 2009 #4

    berkeman

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    Staff: Mentor

    In general, even self-study questions should go into the Homework Help forums. Please keep that in mind. I'll leave this thread here for now, however.
     
  6. Aug 5, 2009 #5
    I apologize. It was a misunderstanding. I will post in the correct part of the forum. Thanks.
     
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