  We reconsider space-time singularities in classical Einsteinian general
relativity: with the help of several new co-ordinate systems we show that the
Schwarzschild solution can be extended beyond the curvature singularity at r=0.
The extension appears as an infinite covering of standard Kruskal space-time.
While the two-dimensional reduction of this infinite sequence of
Kruskal-Szekeres domains obtained by suppressing the angular degrees of freedom
is still a topological manifold - albeit one for which the metric structure is
singular on one-dimensional submanifolds - we obtain for the full
four-dimensional geometry the more general structure of a stratified variety.
