Rigorous model of classical spacetime foam

If in the gravity quantization process one changes from the smooth manifold category to a more general category, qualitatively new features can appear. To illustrate this, we construct a geometrically precise but physically naive model of a classical “spacetime foam” and discuss the consequences of the principle of general covariance and the equivalence principle in this more general setting. We also show how Einstein's equations can be defined on this “spacetime foam”.