 In particular, any globally hyperbolic manifold as defined in 3 is strongly causal.Later Hounnonkpe and Minguzzi proved that for quite reasonable spacetimes, more precisely those of dimension larger than three which are non-compact or non-totally vicious, the 'causal' condition can be dropped from definition 3.In definition 3 the closure of formula_5 seems strong (in fact, the closures of the sets formula_12 imply "causal simplicity", the level of the causal hierarchy of spacetimes which stays just below global hyperbolicity) .