All the interesting cases of homotopy groups of spheres involve mappings from a higher-dimensional sphere onto one of lower dimension. Unfortunately, the only example which can easily be visualized is not interesting: there are no nontrivial mappings from the ordinary sphere to the circle. Hence, . This is because has the real line as its universal cover which is contractible (it has the homotopy type of a point). In addition, because is simply connected, by the lifting criterion, any map from to can be lifted to a map into the real line and the nullhomotopy descends to the downstairs space.