On the topology of stable causality (Q1123432)

According to the authors a subset A of a space-time is called C-convex iff every causal curve between points of A lies entirely in A. Similarly the notion of stable C-convexity is introduced. They characterize the property of a space-time to be (locally or globally) strongly causal or stably causal in terms of these sets. Furthermore the topologies generated by C-convex resp. stably C-convex sets are shown to be \(T^ 1\) iff they are discrete.