A multiply connected set is connected but not simply connected. For an integer 
, a topological
space that is 
-connected
and for which every continuous map from the 
-sphere extends
continuously over the 
-disk is called 
-connected, rather than 
-multiply connected. Here 0-connected means nonempty and pathwise-connected (Hatcher 2002, p. 346).
By Whitehead's theorem, a nonempty CW-complex is 
-connected
for every nonnegative integer 
iff it is contractible
(Hatcher 2002, p. 346).
