the above is from Munkres Topology according to it $ f : U\to S^2$ is continuous and injective and $B$ any closed ball contained in $U$ and $a , b$ two points of $S^2-f(B)$.it says because the identity map $i : B\to B$ is nulhomotopic then map $h : B \to S^2-a-b$ obtained by restricting $f$ is nulhomotopic. but I can't see why? due to what previous lemma or theorem?
I searched a bit and found out that any continuous map from a contractable space to any other space is nulhomotopic but I don't think this has been proved in the book before this theorem?