World function dynamics in generalized spacetimes

A generalization of general relativity is proposed in which the dynamical variable is the two-point distance in a metric space which is not necessarily homoeomorphic to R'', even locally. In the present framework it is possible to compute such things as, for example, the local physical field associated with the Hausdorff dimension, so that the question of the actual value of the dimensionality of spacetime can be meaningfully addressed. (orig.)