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A number of theorems and definitions which are useful in the global analysis of relativistic world models are presented. It is shown in particular that, under certain conditions, changes in the topology of spacelike sections can occur if and only if the model is acausal. Two new covering manifolds, embodying certain properties of the universal covering manifold, are defined, and their application to general relativity is discussed.
Robert Geroch (Sat,) studied this question.