[marksc]

It actually doesn't make sense. A circle with a 1D point missing from its edge is the same as a sphere with a 2D hole in it. Both have material connected "around" it in another dimension. For a sphere the connection wraps around the hole and for a circle the connection wraps around the point (comprising the entirety of the circle's edge).

[PeterisP]

This fails with more than one hole (as I said in the inital comment, two or more). A circle with two 1D points missing breaks apart, a sphere can have an arbitrary number of 2d holes and still be fully connected.