For any two points in a glome, there is a plane containing the two points and the origin. By cutting the glome with the plane we get a great section where we can draw a great ellipse passing through the two points. This means that at any point in a glome we can get to any other point in the glome by going straight.
The shrinking of a loop is the process by which all points in the loop follow straight paths to a specific point. All straight paths towards the specific point intersect only at two points, the specific point and the opposite point of the specific point. Therefore, the order of all points on a loop is not changed during the shrinking.
This means that every loop can be continuously shrunk to a point in a glome. |