 A topological space "X" is said to be "n"-connected (for positive "n") when it is non-empty, path-connected, and its first "n" homotopy groups vanish identically, that is

where formula_2 denotes the "i"-th homotopy group and 0 denotes the trivial group.The requirements of being non-empty and path-connected can be interpreted as (−1)-connected and 0-connected, respectively, which is useful in defining 0-connected and 1-connected maps, as below.The 0-"th homotopy set" can be defined as