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

Weak distinction and the optimal definition of causal continuity