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We prove that global hyperbolicity is stable in the interval topology on thespacetime metrics. We also prove that every globally hyperbolic spacetimeadmits a Cauchy hypersurface which remains Cauchy under small perturbations ofthe spacetime metric. Moreover, we prove that if the spacetime admits acomplete timelike Killing field, then the light cones can be widened preservingboth global hyperbolicity and the Killing property of the field.

Global hyperbolicity is stable in the interval topology