Null-homotopic map

A map is null-homotopic when it is homotopic to a constant map.

A map $f:S^{n-1}\to X$ extends to $D^n$ exactly when it is null-homotopic. An extension contracts radially through the disc; conversely, a null-homotopy descends through the cone quotient $C{S}^{n-1}\cong D^n$.