ABSTRACT
This chapter gives a brief review of elementary causality theory basic to general relativity. It describes an important relationship between the limit curve topology and the C0 topology for sequences of nonspacelike curves in strongly causal space-times. The chapter explains the causal structure of two-dimensional Lorentzian manifolds. Causal space-times exist that contain inextendible nonspacelike curves having compact closure. An inextendible nonspacelike curve which has compact closure and hence is contained in a compact set is said to be imprisoned. The chapter discusses global hyperbolicity. Globally hyperbolic space-times have the important property, frequently invoked during specific geodesic constructions, that any pair of causally related points may be joined by a nonspacelike geodesic segment of maximal length.
