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Homework Help: Connected/Disconnected all the same to me

  1. Dec 16, 2007 #1
    Connected/Disconnected....all the same to me....

    My question for all of you ladies and gentlemen is

    what would be considered as an example of a connected set in R squared that becomes disconnected when we remove one point.

    My answer would be sin(x/2), but is there a simpler example.
  2. jcsd
  3. Dec 16, 2007 #2


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    consider two closed balls with just one point in common.

    Or like you said, a curve that does close in on itself.
  4. Dec 16, 2007 #3
    Huh? I'm confused.

    Would 1/x work? What would be a solid example, one that I could understand?
  5. Dec 16, 2007 #4
    S = f(x; y) : y = 1/x; 0 < x  1g [ f(x; 0) : 1  x  0g would this work
  6. Dec 16, 2007 #5
  7. Dec 16, 2007 #6
    S = {(x,y): y = 1/x, 0 < x [tex]\leq[/tex] 1} [tex]\cup[/tex] {(x,0): -1 [tex]\leq[/tex] x [tex]\leq[/tex] 0}

    I meant would this work?
  8. Dec 16, 2007 #7


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    No, because S isn't connected. Either part of S would work.
  9. Dec 16, 2007 #8


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    Or A= {(x,y)| y= 0} will do.
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