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Simply connected regions

  1. Sep 29, 2009 #1
    Hi,

    I've been reviewing multivariable calculus, which I took ages ago, and trying to understand the concept of a simply connected region. The book I'm reading discusses how the region between two concentric spheres is simply connected, but I'm having trouble seeing it. If I think about that region, and imagine sticking a curve there and shrinking it down, don't I run into trouble when I hit the boundary of interior sphere? Can anyone explain to me how this region is simply connected?

    Thanks.
     
  2. jcsd
  3. Sep 29, 2009 #2

    LCKurtz

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    Once the curve hits the boundary of the interior sphere it can simply slide along that surface to shrink to a point. It doesn't have to just sit at an equator. That extra dimension in which to shrink is what makes it different from the space between two concentric circles in the plane.
     
  4. Sep 29, 2009 #3
    Ok, I see. I was trying to restrict it to a given equator. The same idea then applies to the spiral surface - you can draw your closed curve anywhere on the spiral and let it slide down the spiral to shrink it, right?
     
  5. Sep 29, 2009 #4

    LCKurtz

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