 It was previously well known that any Cauchy surface of a globally hyperbolic manifold is an embedded three-dimensional formula_14 submanifold, any two of which are homeomorphic, and such that the manifold splits topologically as the product of the Cauchy surface and formula_13.In particular, a globally hyperbolic manifold is foliated by Cauchy surfaces.In view of the initial value formulation for Einstein's equations, global hyperbolicity is seen to be a very natural condition in the context of general relativity, in the sense that given arbitrary initial data, there is a unique maximal globally hyperbolic solution of Einstein's equations.