Abstract
Counter-examples are given to Proposition 6.6.7 of Hawking and Ellis, stating the global hyperbolicity of the domain of dependence of a closed achronal set. A corrected and complete statement of this proposition is proposed and the original demonstration of Hawking and Ellis is completed. This modification does not invalidate Hawking's singularity theorem making use of this proposition, since the supplementary condition introduced is still verified in the framework of Hawking's hypothesis.
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