How is the region between two concentric spheres simply connected?

[quasar_4]

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.

 

[LCKurtz]

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.

 

[quasar_4]

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?

 

[LCKurtz]

Yes.