We provide a generalization of global hyperbolicity in pseudo-Riemannian spaces of signature (p, q) for p ⩾ q ⩾ 2. We then prove the compactness of causal diamonds in globally hyperbolic spaces and deduce the existence of solutions to a Plateau problem for this class of spaces. Finally, we describe the topology of globally hyperbolic spaces in a result generalising Geroch's splitting theorem.