 N-connected space

In the mathematical branch of algebraic topology, specifically homotopy theory, n"-connectedness (sometimes, n"-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.To say that a space is "n"-connected is to say that its first "n" homotopy groups are trivial, and to say that a map is "n"-connected means that it is an isomorphism "up to dimension "n," in homotopy".