Multiply connected space

Definition
A topological space is said to be $$n$$-connected for a given $$n \ge 0$$ if its first $$n$$ homotopy groups are trivial. In particular:


 * $$0$$-connected means path-connected space
 * $$1$$-connected means simply connected space

A weakly contractible space is a topological space which is $$n$$-connected for every $$n \ge 0$$.