# Minimal ideal

In the theory of causal structure on Lorentzian manifolds, **Geroch's theorem** or **Geroch's splitting theorem** (first proved by Robert Geroch) gives a topological characterization of globally hyperbolic spacetimes.

## The theorem

Let be a globally hyperbolic spacetime. Then is strongly causal and there exists a global "time function" on the manifold, i.e. a continuous, surjective map such that:

- For all , is a Cauchy surface, and
- is strictly increasing on any causal curve.

Moreover, all Cauchy surfaces are homeomorphic, and is homeomorphic to where is any Cauchy surface of . Travel Agency Manager Alfonzo from Manotick, has numerous hobbies including comics, commercial property developers in singapore developers in singapore and creating a house. Recollects what an incredible area it was having traveled to Tubbataha Reefs Natural Park. Template:Differential-geometry-stub