• Simply connected space
A topological space X is called simply connected if it is path-connected and any loop in X defined by f : S1 → X can be contracted to a point.
http://qindex.info/i.php?x=3534

• Simply connected space
A sphere (or, equivalently, a rubber ball with a hollow center) is simply connected, because any loop on the surface of a sphere can contract to a point, even though it has a "hole" in the hollow center.
http://qindex.info/i.php?x=3577