Assume that $[\alpha]\in\pi_n(X,x_0)$. I want to prove the following:
$[\alpha]=0$ if and only if $\alpha:S^n\rightarrow X$ extends to a map $D^n\rightarrow X$.
Can someone help me with this proof? Is this what some people call: $\alpha$ nullhomotopic iff it factors through $D^n$?
Thanks a lot.