  We show that the definition of global hyperbolicity in terms of the
compactness of the causal diamonds and non-total imprisonment can be extended
to spacetimes with continuous metrics, while retaining all of the equivalences
to other notions of global hyperbolicity. In fact, global hyperbolicity is
equivalent to the compactness of the space of causal curves and to the
existence of a Cauchy hypersurface. Furthermore, global hyperbolicity implies
causal simplicity, stable causality and the existence of maximal curves
connecting any two causally related points.
