Changes

If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a doughnut without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.  

If you draw a circle on a sphere, then you can put a point A inside the circle and a point B outside the circle. The only way to connect A to B would have to cross the circle. So drawing the circle divides the surface of the sphere into two regions. But you can draw a circle around the edge (rim) of a doughnut without creating two regions. You can get from point A on one side of the line to point B on the other side, by going through the hole in the center.  

[[category:mathematics]]

[[category:mathematics]][[Category:Topology]]