  We consider space-times which are asymptotically flat at spacelike infinity,
i^0. It is well known that, in general, one cannot have a smooth differentiable
structure at i^0, but have to use direction dependent structures. Instead of
the oftenly used C^{>1}-differentiabel structure, we suggest a weaker
differential structure, a C^{1^+} structure. The reason for this is that we
have not seen any completions of the Schwarzschild space-time which is C^{>1}
in both spacelike and null directions at {i^0}. In a C^{1^+} structure all
directions can be treated equal, at the expense of logarithmic singularities at
{i^0}. We show that, in general, the relevant part of the curvature tensor, the
Weyl part, is free from these singularities, and that the (rescaled) Weyl
tensor has a certain symmetry.
