Let $p_1 :T_1 \to X$ and $p_2 :T_2 \to X$ be covering. $T_1, T_2$ are path connected spaces, $f : T_1 \to T_2$ is a continuous map, and $p_1=p_2 f$. Please prove $f$ is surjective.
Note:This is an exercise about covering space, the reason make me confused is we only know the definition of covering space and homotopy lift property, another conception such coverings and their fundamental group, monodromy action we have not learn now. So from author's view, only using definition of covering space can solve this question.