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Compact-valued range doesnot imply compact graph

  1. Mar 21, 2008 #1
    y is a correspondence of x. X is compact.
    Can somebody give me an example where y is compacted valued, but the graph(x,y) is not compact.

    A graph will be highly appreciated.
    Last edited: Mar 22, 2008
  2. jcsd
  3. Mar 22, 2008 #2


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    Maybe I'm misunderstanding your question but it seems y(x) = sin x has image [-1,1] yet graph(y) is not compact because unbounded..
  4. Mar 22, 2008 #3
    Quasar 987:
    I just edited my question. Assuming X is compact,....
    The statement is true even though the domain is compact.
    I can tell you are doing physics. I am doing economics, sin function will never cross my mind.
  5. Mar 22, 2008 #4


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    Let me see if I understand what you're asking correctly. You want a function f:X->Y whose domain and range are compact, but whose graph isn't? If this is the case, then (unless you look at non-Hausdorff spaces) you won't be very lucky finding one that is continuous, so try to find that isn't continuous. (Another hint: Try a step function.)
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