A remark on totally vicious space-time (Q1104572)

A space-time \((M,g)\) is called totally vicious if \(I^+(p)\cap I^- (p)=M\) for all \(p\in M\), \(I^+\) and \(I^-\) denoting chronological futures and pasts respectively. The authors prove that this property automatically is satisfied by (M,g), if it is valid for one point of M. [Reviewer's remark: This can easily be shown by a one-line proof directly from the definitions of \(I^+\) and \(I^-\), and is known to most of the experts in causality conditions on space-times.]