

Simply connected space  Wikipedia, the free encyclopedia 
  For instance, a doughnut (with hole) is not simply connected, but a ball (even a hollow one) is. A circle is not simply connected but a disk and a line are. 
  An equivalent formulation is this: X is simply connected if and only if it is path connected, and whenever p : [0,1] → X and q : [0,1] → X are two paths (i.e.: continuous maps) with the same start and endpoint (p(0) = q(0) and p(1) = q(1)), then p and q are homotopic relative {0,1}. 
  If a space X is not simply connected, one can often rectify this defect by using its universal cover, a simply connected space which maps to X in a particularly nice way. 
 en.wikipedia.org /wiki/Simply_connected_space (931 words) 
