  In view of the well-known correspondence between gravitational fields and
space-time distributions on a world manifold X, the criterion of gravitation
singularities as singularities of these distributions is suggested. In the germ
terms, singularities of a (3+1) distribution look locally like singularities of
a foliation whose leaves are level surfaces of a real function f on X. If f is
a single-valued function, changes of leave topology at critical points of f
take place. In case of a multi-valued function f, one can lift the foliation to
the total space of the cotangent bundle over X, then extend it over branch
points of f and project this extension onto X. Singular points of this
projection constitute a Lagrange map caustic by Arnol'd.
