Question

Proof that Minkowski spacetime is globally hyperbolic?

Answer 1

The causal future and past of Minkowski space are just cones along the time axis, perhaps you could show that the intersection of any two such cones is a closed set.

Answer 2

Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.[1]