A space-time structure is called integrable if a spatial distribution F is involutive. In this case, its integral manifolds constitute a spatial foliation of a world manifold whose leaves are spatial three-dimensional subspaces. A spatial foliation is called causal if no curve transversal to its leaves intersects each leave more than once. This condition is equivalent to the stable causality of Stephen Hawking. A space-time foliation is causal if and only if it is a foliation of level surfaces of some smooth real function on X whose differential nowhere vanishes. Such a foliation is a fibred manifold X → → R . However, this is not the case of a compact world manifold which can not be a fibred manifold over R .