On defining functions and cores for unbounded domains. III

We extend the authors' results on existence of global defining functions to a number of different settings. In particular, we relax the assumption on strict pseudoconvexity of the domain to strict q-pseudo-convexity and we consider more general situations, where the ambient space is an almost complex manifold or a complex space. We also investigate to what extent the assumption on smoothness of the boundary of the domains under consideration is necessary in our results.