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Homework Help: Continuous function sends closed sets on closed sets

  1. Aug 8, 2006 #1
    Let [tex]f: D \rightarrow \mathbb{R}[/tex] be continuous.

    Is there an easier function that counterexamples;
    if D is closed, then f(D) is closed
    than D={2n pi + 1/n: n in N}, f(x)=sin(x) ?????


    Plus, these counterexamples are very similar ...but are they correct?

    If D is not closed, then f(D) is not closed.
    CE: D = (0, 1) and f(x) = 5
    If D is not compact, then f(D) is not compact.
    CE: We use same CE as above
    If D is infinite, then f(D) is infinite.
    CE: D = all real numbers and f(x) = 5
    If D is an interval, then f(D) is an interval
    CE: Use same CE as first
     
    Last edited: Aug 8, 2006
  2. jcsd
  3. Aug 8, 2006 #2

    matt grime

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    Don't double post.
     
  4. Aug 8, 2006 #3
    Couldn't figure out how to delete these mofo's.....so anything to add to my question....?
     
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