Simply connected space
A space (or shape) is called simply connected if it is all one piece and does not have any "holes" that pass all the way through it. For example, a ball is simply connected, but a doughnut is not.
More formally, being "one piece" means a shape is path-connected, which means there is a path from any point inside the shape to any other which does not leave the shape.
Simply Connected Space Media
This shape represents a set that is not simply connected, because any loop that encloses one or more of the holes cannot be contracted to a point without exiting the region.
A sphere is simply connected because every loop can be contracted (on the surface) to a point.
A torus is not a simply connected surface. Neither of the two colored loops shown here can be contracted to a point without leaving the surface. A solid torus is also not simply connected because the purple loop cannot contract to a point without leaving the solid.
