  We describe a topological predual to differential forms constructed as an
inductive limit of a sequence of Banach spaces. This subspace of currents has
nice properties, in that Dirac chains and polyhedral chains are dense, and its
operator algebra contains operators predual to exterior derivative, Hodge star,
Lie derivative, and interior product. Using these operators, we establish
higher order divergence theorems for net flux of k-vector fields across
nonsmooth boundaries, Stokes' theorem for domains in open sets which are not
necessarily regular, and a new fundamental theorem for nonsmooth domains and
their boundaries moving in a smooth flow. We close with broad generalizations
of the Leibniz integral rule and Reynold's transport theorem.
