 An example of a non-maximally extended spacetime can be easily had, along with a sense of why they intuitively seem in some way or other deficient. For the moment, imagine spacetime is only two-dimensional, and flat, like an endless sheet of paper. Now, excise from somewhere on this plane a closed set shaped like Ingrid Bergman. Any path that had passed through one of the points in the removed set is now incomplete. 