Weak distinction and the optimal definition of causal continuity

Abstract

Causal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can actually replace distinction in the definition of causal continuity. An intermediate proof shows that feeble distinction and future (past) reflectivity implies past (resp. future) distinction. Some new characterizations of weak distinction and reflectivity are given.