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.

9 pages, 2 figures. v2: improved and expanded version. v3: a few misprints have been corrected and a reference has been updated

References in corpus (3)

• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• The causal ladder and the strength of K-causality. II
• The causal ladder and the strength of K-causality. I

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• Widening the light cones on subsets of spacetime: some variations to stable causality