Compact-valued range doesnot imply compact graph

  • Thread starter CHatUPenn
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  • #1
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Main Question or Discussion Point

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.
 
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  • #2
quasar987
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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..
 
  • #3
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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.
Cheers
 
  • #4
morphism
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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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