given a bundle $E$ and a base space $X$ is we have a projection $\Pi: E \rightarrow X$. then is $\Pi^{-1}$ a surjective mapping?
I ask this because in the case of mobius strip the base space is $S^1$ and the fibre is a line so $F=\Pi^{-1}(x)$ where $F$ is the fiber should give the fiber. but it can't so it should give a point on the fiber. and $\Pi^{-1}$ can not be on to.