Hey guys, I've often seen in the definition of a Fiber bundle a projection map [itex]\pi: E\rightarrow B[/itex] where E is the fiber bundle and B is the base manifold. This projection is used to project each individual fiber to its base point on the base manifold. I then see a lot of references to the inverse of this projection map. It seems to me, that in general, this map should be many to one, since it should project a whole fiber to its base point. In this case, how can one define an inverse to this map? It seems odd to me that there can be an inverse to a many to one mapping...or have I missed something basic?