  A system of differential forms will establish a topology and a topological
structure on a domain of independent variables such that is possible to
determine which maps or processes acting on the system are continuous. Perhaps
the most simple topology is that generated by the existence of a single 1-form
of Action, its Pfaff sequence of exterior differentials, and their
intersections. In such a topology the exterior derivative becomes a limit point
generator in the sense of Kuratowski. The utilization of such techniques in
physical systems is examined. A key feature of the Cartan topology is
determined by the Pfaff dimension (representing the minimum number of functions
to describe the 1-form generator). In particular, when the Pfaff dimension is 3
or more the Cartan topology becomes a disconnected topology, with the existence
of topological torsion and topological parity. Most classical physical
applications are constrained to cases where the Pfaff dimension is 2 or less,
for such is the domain of unique integrability. The more interesting domain of
non-unique solutions requires the existence of topological torsion, and can
lead to an understanding of irreversible processes without the use of
statistics.
