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WHat's wrong in my argument?

  1. Jun 13, 2007 #1
    I was asked to prove, every punctured open set in R^2 is path connected.

    My argument : take points x and y. let z be the point we've taken off from U (open).
    if x, y,z do not pass through a staright line, we have a segment between a and y.
    Now if the 3, i.e. x,y,z lie on a straight line...then pick another point ,say p, not lying on the staright line.
    we have segments joining x and p and p and y. hence, we've found a path between x and y ,as required.

    apparently, this is wrong...my prof told me not bring in straight lines anywhere! any hints?? thanks!
  2. jcsd
  3. Jun 13, 2007 #2
    What if your set is not convex?
  4. Jun 13, 2007 #3


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    Can you show that there's a 'path' that circles the puncture?
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